I would like to think that Starfleet has somewhat more stringent requirements than the modern military or university, given that you're potentially representing not only humanity, but hundreds of other races throughout the galaxy, to say nothing of the fact that many captains would have enough fire power at their disposal to lay waste to entire populations. So putting aside those lives that are directly under your command and looking at the bigger picture of the actual responsibility that rests on your shoulders, I somehow doubt that most people would make the cut.
So no, I could not be a captain.
That being said, they let Barclay join with all his instabilities and Troi passed the command test...they even made Crusher a captain in an alternate timeline...though she did promptly get her ship destroyed, so there you go. So who knows, maybe they just hand out ships like a reward system for time served.
All in all, Starfleet should have better standards given their importance in representing the Federation.