I don't think I would believe he was a prophet, but if I were to believe that he was, the main reason would probably be the Qur'an—from a linguistic standpoint, not a theological or philosophical one.
Classical Arabic poetry is immensely excellent in terms of its eloquence, vocabulary, and grammar, yet the Qur'an easily surpasses it. Some of the greatest Arab poets lived before and during Muhammad's time, and a lot of them were non-Muslims. Yet they couldn't outclass the linguistic brilliance of the Qur'an. It's also not an entirely subjective matter, since the Arabic language has more or less standard criteria for determining what is or isn't linguistically outstanding. Grammar is one criterion; many Arabic poems contain grammatical mistakes. The Qur'an doesn't. This includes sometimes compromising grammatical rules for the sake of "poetic liberty," but the Qur'an doesn't do that in a single one of its 114 surahs.
Also, Arabic literature and poetry became heavily influenced by the Qur'an, which indicates that its linguistic value is not just a matter of subjective opinion. Basically, if you want to give an example of correct usage of a grammatical, poetic, or rhetorical rule in Arabic, you use the Qur'an before anything else. It's no easy feat for a book to remain the primary reference for a language as complex as Arabic over the span of fourteen centuries.
Another one of the Qur'an's unique features is that it has seven main different readings depending on placement of diacritics and, sometimes, placement of letters. This might sound ordinary at first, but what I find most interesting about it is that all of the different readings make sense in context. They weren't just made up for the sake of multiplying the number of possible ways to read the Qur'an; they're merely an expansion of the linguistic depth of the Qur'an.
Personally, I don't think that achieving a remarkable feat in any given field, be it poetry or science or anything else, necessarily justifies a claim of prophecy, but what I'm saying here is that I don't share some people's view that considering the Qur'an a sign of prophecy is insane or something. I think a case could be argued for it—granted, not necessarily a convincing case, but definitely not necessarily an "insane" one either. The Qur'an is, simply put, beyond phenomenal as far as language goes.