The idea that the author of the Gospel of Matthew presents Jesus' teachings in the Sermon on the Mount——particularly in the so-called Six Antitheses——as teachings that are not meant by Jesus to be followed by his disciples seems to be based on at least two of the following suppositions:
(1) The presumption that the scribes and Pharisees kept the Torah perfectly or at least as perfectly as one could keep it. If Jesus requires a righteousness greater than that exhibited by the scribes and Pharisees to even enter the kingdom of heaven (5:20), then perhaps Jesus does not actually expect for his disciples to exhibit a greater righteousness.
(2) The interpretation that Jesus' "I say to you" teachings go far beyond the teachings of the Torah and the Prophets. Likewise, if Jesus demands for an idealistic behavior far exceeding what is taught in the Torah and the Prophets, then perhaps Jesus is suggesting that no one can exhibit a righteousness fit for the kingdom of heaven by observing what can be learned from the Torah and the Prophets, regardless of how they are interpreted.
(3) The observation that rhetorical/hyperbolic language or figures of speech appear in the Sermon on the Mount. In addition to the above, if Jesus uses rhetoric, hyperbole, or figures of speech to communicate his message, then perhaps even his message is to be regarded as nothing more than rhetoric and is thus to be unheeded by his followers.
To answer the OP's question, I will deal with these suppositions respectively to show their problems and as a result to demonstrate that Jesus is presented as expecting his disciples to follow his teachings.
RESPONDING TO THE SUPPOSITIONS
(1) The Righteousness of the Scribes and Pharisees
"The scribes and Pharisees" are not presented in the Gospel of Matthew favorably or as those who observe the Torah well, but just the opposite. In Matthew 23:23, Jesus rebukes "the scribes and Pharisees" for neglecting to observe what is "heavy" of the Torah, namely justice, mercy, and faithfulness. In 23:29–36 Jesus accuses them of being "descendants" of those who murdered the prophets because he says they will murder some prophets, sages, and scribes that he will send. In 15:1–9 Jesus rebukes "the scribes and Pharisees" for breaking the commandment to honor one's father and mother. Those are two of the Ten Commandments that "the scribes and Pharisees" are said to be (or will be) guilty of breaking. Further, in 19:18 Jesus lists "You shall not murder" and "You shall not commit adultery" as two examples of commandments to observe to inherit eternal life. This failure to observe even the most fundamental of commandments appears to be why Jesus warns his disciples and those listening that unless their righteousness exceeds that of "the scribes and Pharisees" they will not enter the kingdom of heaven. [Note BTW that in 19:18, the first (murder), second (adultery), and sixth (love your neighbor) commandments listed are also the first, second, and sixth "You have heard that it was said" commandments listed in 5:21-28.]
(2) Jesus' "I Say to You" Teachings:
As opposed to popular opinion, I propose that Jesus' "I say to you" teachings are allusions and derivations of commandments/statements in the Torah. Due to space, I will not show that this is the case for all of his "I say to you" teachings here, but I will demonstrate this for vv. 27–30, since these verses are considered to be of those most problematic in the OP.
Let us first consider the immediate context, vv. 19-20.
Matthew 5:17-20 (NRSV):
17 Do not think that I have come to abolish the law or the prophets; I have come not to abolish but to fulfill. 18 For truly I tell you, until heaven and earth pass away, not one letter, not one stroke of a letter, will pass from the law until all is accomplished. 19 Therefore, whoever breaks one of the least of these commandments, and teaches others to do the same, will be called least in the kingdom of heaven; but whoever does them and teaches them will be called great in the kingdom of heaven. 20 For I tell you, unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven.
According to these verses, who is considered to be great in the kingdom of heaven? It is whoever does and teaches "the least of the commandments" of the Torah (and Prophets). Therefore, according to this passage, whoever does and teaches "the least of the commandments" would surely exhibit a righteousness exceeding that of "the scribes and Pharisees". This contrast is especially interesting while keeping in mind that Jesus rebukes "the scribes and Pharisees" in 23:23 for neglecting to observe what is "heavy" (βαρύς) of the Torah. This rebuke implies that "the scribes and Pharisees" to whom he refers do what is "light" of the Torah. Why does Jesus emphasize "the least of the commandments" rather than "the heaviest of the commandments" as he does in 23:23? To answer this question we need to notice that Jesus does not use the technical language of "heavy" or "light" in 5:19 as he does in 23:23 or as it is used in the rabbinic literture. Instead, Jesus uses the term "least" (ἐλάχιστος) which is used in 25:40, 45 rhetorically to refer to those treated or considered "least" by others but not by Jesus. Similarly, the term "great(est)" is used rhetorically in 18:1-5; 20:25-28; 23:11 to refer to those whom Jesus would consider great but not by others, or vice versa. Based on these observations, it seems that the reason Jesus uses the expression "the least of the commandments" is because he is using the phrase rhetorically to refer to commandments in the Torah that are treated or considered to be least by others but not by him.
What are some examples of these "least of the commandments" in the Torah? In my assesment, Jesus provides six examples of them in his "I say to you" teachings. Here is one of them as a test case for my proposal.
Matthew 5:27-30 (NRSV):
“You have heard that it was said, ‘You shall not commit adultery (οὐ μοιχεύσεις).’ 28 But I say to you that everyone who looks at a woman (γυναῖκα) with lust (ἐπιθυμῆσαι αὐτὴν) has already committed adultery (ἤδη ἐμοίχευσεν) with her in his heart. 29 If your right eye causes you to sin, tear it out and throw it away; it is better for you to lose one of your members than for your whole body to be thrown into hell. 30 And if your right hand causes you to sin, cut it off and throw it away; it is better for you to lose one of your members than for your whole body to go into hell.
Commentators recognize that the "you have heard that it was said" commandment that is referenced is one of the Ten Commandments (Ex. 20:14//Deut. 5:17). But what some——even most——commentators miss or ignore is that Jesus' "I say to you" teaching is an allusion and derivation of another one of the Ten Commandments:
Deut. 5:21//Ex. 20:17:
וְלֹא תַחְמֹד אֵשֶׁת רֵעֶךָ (MT)
οὐκ ἐπιθυμήσεις τὴν γυναῖκα τοῦ πλησίον σου. (LXX)
“You shall not covet your neighbor’s wife." (NRSV, NETS)
There are a few things to notice:
(i.) Jesus is not talking about sexual immorality in general (πορνείας); he is talking specifically about committing adultery (μοιχεύω).
(ii.) The Greek word translated as "woman" in Matt 5:28 can equally be translated as "wife". Notice it is the same word in LXX Deut. 5:21//Ex. 20:17. Because adultery--not sexual immorality or fornication--is the topic, "wife" is at least the primary referent.
[FOOTNOTE: The possible exception of which I am thinking is an otherwise eligible bachelorette pursued by a married man. Jesus' teaching on divorce in 19:9 implies that polygamy is forbidden by him, so perhaps γυναῖκα could also include this situation.]
(iii.) The Greek verb translated as "lust" in Matt. 5:28 and as "covet" in Deut. 5:21//Ex. 20:17 is the same Greek verb, though in a different form: ἐπιθυμέω (epithuméo).
Due to the lexical connections of γυναῖκα ("wife/woman") and ἐπιθυμέω ("to desire, long for, covet, or lust for"), and because of the contextual connection of adultery, it should be evident that Jesus is alluding to the "tenth" of the Ten Commandments, according to at least Jewish and Protestant numbering.
Therefore, Jesus is not "raising the bar" of required righteousness, but is expositing what Torah fully requires from an informed understanding of it. Torah not only forbids adultery, it also forbids coveting a neighbor's wife. As a result, Jesus is inferring from this that adulterous lust is already committing adultery in the heart. Notice the specificity. He is not redefining adultery. He is simply pointing out by inference from the "tenth" commandment that adultery begins in the heart with adulterous lust.
That is, those who want to be great--and especially those who already consider themselves to be great--in the Kingdom of God are expected by Jesus to not only not commit adultery but also to not covet their neighbor's wife. These are actual commandments in the Torah, not rhetorical ones.
(3) Rhetorical Language to Convey the Message:
As we have already seen, Jesus does seem to use rhetorical language at times to convey his message, such as the terms "least" and "great(est)" and the phrase "the least of the commandments".
Most notably is the dramatic language of vv. 29–30.
Matthew 5:29–30 (NRSV):
29 If your right eye causes you to sin, tear it out and throw it away; it is better for you to lose one of your members than for your whole body to be thrown into hell (γέεννα). 30 And if your right hand causes you to sin, cut it off and throw it away; it is better for you to lose one of your members than for your whole body to go into hell (γέεννα).
The evocative language is probably hyperbole to communicate his point and its importance.
Compare, for example, the following passage:
Proverbs 23:2 (NRSV):
and put a knife to your throat if you have a big appetite (אִם־בַּעַל נֶפֶשׁ אָתָּה).
Notice the similarity of language. It is a figure of speech to convey the message "curb your appetite". Though the language that is used is rhetorical or hyperbole, the message is not.
Similarly, the graphic language of vv. 29–30 is a word picture to convey a similar point: "curb your desire". Notice that Jesus speaks of cutting off and gouging out the right hand and right eye rather than both hands and eyes. This might be symbolic. Also notice that although the dramatic actions are probably hyperbole, the concluding point is not. It is indeed better to lose one's right eye or one's right hand than to lose the whole body. Adulterous lust leads to adultery, which is punishable by death. Jesus might be implying this point and/or that the court of heaven will judge the adulterous lust like the court of earth judges adultery. Nevertheless, the end result of adulterous lust is "Gehenna". The language in these verses appears to be rhetorical since it is a word picture, but like Prov. 23:2 and like the language of "the least of the commandments" it is language used to convey a real point: curb your desire otherwise the end result will be death/Gehenna.