The ship underwater made no sense to me either.
They have a hangar full of shuttles (and since aquashuttles were present on the original Enterprise, it is safe to assume the JJprise would have them as well, given that it is three times the size) and several fully functional transporter pads, all of which have been used countless times on planetary survey missions.
This was just like the buggy in Nemesis, something that's never been seen in Trek before so therefore it must be new, different and cool. Totally pointless I found.
Then there is the native species. They had to avoid contact with them, so as to ensure they culture and social identity wasn't contaminated by Starfleet. How better to do that then by flying into their atmosphere only a few short kilometers away from one of their major temples, just to hide in the sea, then have to take off again and back into orbit, all without being seen! What?