It could also be, in part, because if it was lowercase people would try to say it instead of spelling out the letters.
People will often say “gyno” instead of gynecologist, if just talking about that.
PhD is an "almost initialism" :P and would be very hard to read without spelling out the letters.
MD, DDS and DO are initialisms and there's no other way to read it.
ObGyn is more of an acronym and it would make sense to read it as a word.