The problem with the Enterprise being under water (for me..anyway) is it's never really explained why it is there, we just have to accept that it's just..well..under water. Why not simply be in orbit like any other mission? Why risk exposing a primitive society to an advanced technological achievement like the Enterprise? There are tons of questions, but I guess in the end we just have to accept the fact is was there for a cool shot of the Enterprise coming out from an ocean.
You just answered your own question. The movie explained quite well why the ship was underwater, and I don't really understand why so many people keep asking that question.
The ship was under water because it served the plot of the movie. If Kirk had the ship in orbit, then there would be no chance for the natives to see it. The whole point of them being able to see the ship was proof that Kirk was an inexperienced captain whose command should be taken away from him for recklessness. I mean, that was half the freaking movie's plot!
Edit: Charles Phipps above me essentially says the same thing I did.