Because it is not the Same Key(s) Being Referenced
The "key of the house of David" (Isaiah 22:22 LXX, Brenton) and "key of David" (Rev. 3:7, ESV) are referring to the same "key" (singular), the same concept. But "the keys to the kingdom of heaven" (Matt. 16:19, ESV) is not the key of David. To equate the two would probably be similar to (and this is from the point of view of a United States citizen) having the "key to the White House" (i.e. Presidency) being equal to having "the keys to all the prison cells in the United States" (i.e. the power to loose or bind prisoners).
Discussion of Relevant Textual Issue
Note that Matthew 16:19 has variant readings at the point of the word in question, κλείς ("key"), a grammatically gendered feminine noun:
δώσω σοι τὰς κλεῖδας τῆς βασιλείας τῶν οὐρανῶν, καὶ ὃ ἐὰν δήσῃς ἐπὶ
τῆς γῆς ἔσται δεδεμένον ἐν τοῖς οὐρανοῖς, καὶ ὃ ἐὰν λύσῃς ἐπὶ τῆς γῆς
ἔσται λελυμένον ἐν τοῖς οὐρανοῖς. (NA28)
The above treats the word in the basic third declension format where the accusative plural is an ‑ας ending.
Καὶ δώσω σοὶ τὰς κλεῖς τῆς βασιλείας τῶν οὐρανῶν· καὶ ὃ ἐὰν δήσῃς
ἐπὶ τῆς γῆς, ἔσται δεδεμένον ἐν τοῖς οὐρανοῖς· καὶ ὃ ἐὰν λύσῃς ἐπὶ τῆς
γῆς, ἔσται λελυμένον ἐν τοῖς οὐρανοῖς. (Robinson & Pierpont, Byzantine
Majority Textform 2005)
The above treats the word in the contracted third declension format where the accusative plural ends up with an ‑εις, which the contraction in this word sees a change in accent—the singular has the acute (κλείς) and the nominative/accusative plurals have the circumflex (κλεῖς).
Note that in an unaccented text, like many of the earlier Greek manuscripts, other clues would have to indicate if κλεις (without any accent) were singular or plural. Such clues are present in this text, as the article τὰς is only accusative plural.
So despite the variant reading, there is no doubt the plural is intended in Mt 16:19 (see also Rev 1:18 for a similar construction, even in the NA28 text).
That it is singular in the Isa 22:22 LXX (τὴν κλεῖδα) and Rev 3:7 (τὴν κλεῖν; no variant here) is also clear, even though the Isaiah passage follows the basic declension form while the Revelation passage follows the contracted form. Again, the article helps as τὴν is accusative singular.
The Reason for Plural and Relationship of the Keys
It would become too theological and unproductive to diverge into discussions about "the kingdom" (and there are many discussions about things related to the kingdom (even more than this link indicates)). But some comment about it is important to differentiate it from the house of David, since you state in your question that "in Matthew 16 Jesus refers to the Key(s) of David as being plural," when in fact the verse mentions nothing about David at all.
I believe this improper equation forms the basis of your confusion with the verse that elicited your question.
To say "'the key of' something" refers in a figurative sense to that which locks/unlocks access to, or gives one control of that something (just as a literal key gives access to a place, or allows one to have control of what is behind the lock). So the two things being referred to are:
- Control of the Davidic house, that is, the supreme rulership from the line of David and his descendents, but also then over that line (i.e. individual rulership both over the house itself and rulership of the house over the kingdom through this individual).
- Access to the kingdom of heaven/God—for sake of argument here, this appears to be true however one wants to perceive the kingdom and gaining access to it.
Note how an important cross reference to the Davidic house distinguishes the house from the kingdom. 2 Sam 7:16 (ESV) states in God's promise to David:
And your house and your kingdom shall be made sure forever before me.
Your throne shall be established forever.
So Jesus is the one given the key of David (as Rev 3:7 and other passages indicate his relation to David). He is the one to be in control of the house and the kingdom. Having this position of authority, Jesus in Mt 16:19 is granting a different authority to Peter (and some would argue by extension to all believers... but that is another theological track that need not be followed for the answer here).
This authority involves the use of many keys, as apparently each binding/loosing needs its own key. Similar language to what these keys do is used in Mt 18:18, in context (see v.1-20 for whole context) with respect to entrance to the kingdom and fellowship in the church. It may also be connected to John 20:23 with respect to the forgiveness of sins (this connection is not as direct, and establishing the validity or not of this connection with the keys of Mt 16:19 is not necessary for the discussion here).
The important point here is that Matthew 18 (and John 20 if such is taken as evidence) show that what is bound/loosed is in relation to various individuals (hence multiple keys) and in turn their individual relation to the kingdom. This authority is entrusted to the Peter/the church. In contrast, the key of David is in relation to a single individual and that One's authority within the ruling house of Israel, which authority the New Testament argues belongs only to Jesus Christ.
So Matthew is not referencing the key of David that the other two passages you reference refer to. There is no specific relationship having to do with the Greek texts themselves other than they both use the Greek vocabulary word "key" to relay the concepts they are speaking about.