Unfortunately, I didn't know Michelangelo personally, but I would guess, If he didn't want to show Davids private parts... He would have covered it with a fig-leaf or something else.
Sooooo... the question now is: Was Michelangelo some kind of early Pornograph?
And what about so many old and long decayed artists: Was their art some kind of early pornography in disguise?
(On a serious note, I don't think that michelangelo didn't solely intent to show Davids private parts... But they became certainly a prominent part of David for the world to see... I'd even dare say, Davids private parts are the most famues p. parts in the world. After mine, that is...)