It's not just reasonable, but according to Greek scholar Kenneth McKay, those who have only "a smattering of Greek" and see some sort of "magic" in the words use the words "I am" and not some form of the English perfect (e.g. have been). See the article, Kenneth McKay, "I AM" in John's Gospel and also a link to the paper online.
Kenneth L. McKay graduated with honors in Classics from the Universities of Sydney and Cambridge, taught Greek in universities and theological colleges in Nigeria, New Zealand, and England, who taught at the Australian National University for 26 years, has written numerous articles on ancient Greek syntax, as well as authored a book on Classical Attic, Greek Grammar for Students, and A New Syntax of the Verb in "New Testament Greek: an aspectual approach", provides the following in relation to the alleged "true parallel between Exodus 3:14 (LXX) and John 8:58"
"I am" in John's Gospel
The Expository Times, 1996, page 302 BY K. L. MCKAY, MA,
FORMERLY OF THE AUSTRALIAN UNIVERSITY
It has become fashionable among some preachers and writers to relate Jesus' use of the words "I am" in the Gospel according to John, in all, or most, of their contexts, to God's declaration to Moses in Exodus 3:14, and to expound the passages concerned as if the words themselves have some kind of magic in them. Some who have no more than a smattering of Greek attribute the "magic" to the Greek words ego eimi. 1 I wish briefly to draw attention to the normality of the Greek in all such passages, and the unlikelihood of the words ego eimi being intended to suggest any special significance of this kind.
It is, of course, perfectly reasonable to draw attention to Jesus' claims about himself by noting the "I am" element common to them: 'I am the bread of life' (6:35), 'I am the light of the world' (8:12), 'I am the gate/door' (10:7), 'I am the good shepherd' (10:11), 'I am the resurrection and the life' (11:25), 'I am the way, the truth and the life' (14:6), 'I am the true vine' (15:1). These statements give important insights into the identity and work of Jesus, and we can be challenged to decide whether the words "I am" in them convey truth, delusion, deceit, or something else.
In each case the Greek words used are ego eimi, the pronoun being emphatic (as is usually appropriate in beginning a startling fresh statement, answering a question of identity or personal activity, and in some other circumstances), and the verb, also slightly emphatic,  being the normal use of the verb 'to be' as a copula, the means of linking the subject with the significant words, 'bread', 'light', etc., which occur as noun complements. The same principle applies when the complement is an adjective or an adverb or adverbial phrase used adjectivally.
With variations of context the degree of emphasis may vary, and either the pronoun or the verb may be omitted. In the parallelism of 8:23 pronoun and verb are separated: humeis ek ton kato este, ego ek ton ano eimi, but in the immediately following parallel statement the introduction of a negative brings the verb forward (thus also giving extra emphasis to toutou): ego ouk eimi ek tou kosmou toutou. In 14:10 the verb is omitted, because it is understood from the rest of the sentence: ego en tw patri kai ho pater en emoi estin.  In 14:20 a development from the same statement, also in a hoti clause, omits the copula entirely: ego en tw patri mou kai humeis en emoi kagw en humin. In 10:36 the personal pronoun is not needed for emphasis, and is omitted: huios tou theou eimi. In 7:34 and 7:36 the clause structure demands the postposition of the subject: hopou eimi ego humeis ou dunasthe elthein.
Although the natural English translations differ, there are two contexts of this kind in which Jesus uses the words ego eimi alone to identify himself: in 6:20, where the disciples are afraid of the apparition they see walking on the water, and Jesus reassures them by identifying himself, quite naturally, with these words, which translate into English as "It is I" and in 18:5, while Jesus acknowledges that he is Jesus of Nazareth by speaking the same words, which are naturally translated into English as "I am he".
The syntactic difference between them is that in the former ego is the complement, the unexpressed subject being something equivalent to 'what you see', and in the latter ego is the subject, the unexpressed complement being 'Jesus of Nazareth'. In both these passages ego eimi is the natural Greek response  in the circumstances, as may be seen in 9:9, where the man cured of blindness uses exactly the same words to acknowledge his identity. The dramatic reaction of the arresting party in 18:6 is readily explained if we note that the confident authority of Jesus' presence was such that he defeated the merchants in the temple (2:15), and he simply walked away when the crowd was intent on throwing him over the brow of the hill near Nazareth (Luke 4:28-30).
The verb 'to be' is used differently, in what is presumably its basic meaning of 'be in existence', in John 8:58: prin Abraam genesthai ego eimi,  which would be most naturally translated 'I have been in existence since before Abraham was born',  if it were not for the obsession with the simple words 'I am'. If we take the Greek words in their natural meaning, as we surely should, the claim to have been in existence for so long is in itself a staggering one, quite enough to provoke the crowd's violent reaction.
For the emphasis on the words 'I am' we need to look back to God's words to Moses in Exodus 3:14, 'I am who I am. This is what you are to say to the Israelites: "I am has sent me to you".' The passage in its Hebrew form has been discussed by many commentators as something of a problem, with possibilities that the verb could mean 'I am', 'I will be', 'I become', or 'I will become', and the pronoun 'that', 'who', 'what', or even 'because'. Some see a need to emend the text, and some stress various critical principles as basic to its interpretation. A few refer to the Septuagint translation of the passage as relevant for understanding it. 
Now the Septuagint was the translation done for the benefit of the increasing number of Greek-speaking Jews a couple of centuries earlier, so naturally it is the version of the Old Testament that is normally referred to in the New Testament, and certainly the one most likely to be known to the early readers of John's Gospel.
It's translation of Exodus 3:14 follows the sense (as understood by the Jewish translators) rather than the exact form of the Hebrew: ego eimi ho wn ... Ho wn apestalke me, which translates into English literally as 'I am the being one','  and 'the being one has sent me'. Now the words ego eimi here are the emphatic pronoun and the copula as in most of the passages cited above; and ho wn represents a relative clause which in its first occurrence would be hos eimi and in its second occurrence would be hos esti,  but the most natural translation into English of both would be 'the one who is (who really exists)','  the verb having its basic meaning (and being so accented), and not being a mere copula In neither is there any possibility of inserting an emphatic ego.
So the emphatic words used by Jesus in the passages referred to above are perfectly natural in their contexts, and they do not echo the words of Exodus 3:14 in the normally quoted Greek version. Thus they are quite unlikely to have been used in the New Testament to convey that significance, however much the modern English versions of the relevant passages, following the form of the Hebrew words, may suggest it.
1 I have seen one such speaker try to impress his audience by writing the words on a blackboard, only to demonstrate that he was ignorant of even the simplest details of Greek.
 It's position is un-emphatic, but the degree of emphasis could be reduced by its omission, which would make no difference to the meaning. The omission of the copula is quite common in Greek, especially, but not exclusively, in the third person.
 The fact that this is a reported statement, in a hoti clause, does not affect the grammar, but only the degree of emphasis.
 In translation, if as is likely, the original reply was the equivalent in Aramaic.
 Note that with this meaning the verb is differently accented in Greek [ E)GW\ E)MI/ instead of E)GW\ E)IMI ].
 For the construction see "K. L. McKay, A New Syntax of the Verb in New Testament Greek: An aspectual approach" (Peter Lang, 1994), 4.2.4.
 For extensive modern discussion of the problems of interpretation see Brevard S. Childs, Exodus: A Commentary (OTL, SCM, 1974) and John 1. Durham, Exodus (WBC 3, Word, 1987). See also Martin Noth, Exodus (OTL, SCM, 2nd ed. 1966); U. Cassuto, Commentary on the Book of Exodus (Magnes Press), 1. P. Hyatt, Exodus (NCB, Oliphants, 1971); Alan Cole, Exodus (TC, IVP, 1973); J. W. Wevers, Notes on the Greek Text of Exodus (Scholars Press, 1990).
 As Noth mentions in a footnote.
 Cf. the Vulgate translation of 14b: Qui est misit me ad vos.
 English has lost the full range of inflections, and the relative pronoun is now treated as if it were always third person.