There are multiple references to communication problems and atmospheric disturbance (due to the volcanic eruptions) causing transporter difficulties. As we see, it seems perfectly possible for the Enterprise to communicate with the Shuttle from under the water, so the most likely reason for taking the Enterprise into the atmosphere was to allow continual communication with the away team from under the disruptive atmospheric layer.
Q: The Enterprise is hiding submerged—Why? What about waiting in orbit for the return of the away team? Why beaming is not possible?
Why it is not possible to beam Mr. Spock out of the vulcan, when it is
later possible to (trans-)beam from earth to Qo’noS?
Robert Orci: Line of sight necessary given unstable and shifting magnetic field of super volcano on alien planet. That’s why no
beaming. Gotta physically get back to the ship
Into Darkness' co-writer Bob Orci drops by TrekMovie to answer a few questions
Once that decision was taken, they then needed to find an area that was close to the drop zone, that permitted communication, that allowed the crew to freely enter and leave the ship while conducting science surveys and that wouldn't be subject to observation by the locals. Evidently after scouring the land surface they couldn't anywhere that met their requirements and were forced to improvise, finally settled for taking the ship a hundred or so feet underwater.
Out of Universe
The goal was to present the opening shot of the Enterprise in a new and exciting way. The writers evidently decided that "coming up from underwater" was simply something that audiences hadn't seen before and wouldn't be expecting.
Alex Kurtzman: Well without revealing too much what I can tell you is that in the same spirit as “can the Enterprise be under water? What does that mean? How are we going to justify this? How are we going to explain it?” We went back and we talked a lot about things that made us want to make the first movie in the first place as fans. And what do we feel was successful for the fans. A lot of that had to do with honoring the history — honoring the show. But we also want to come up with a way to make the stories feel fresh and unpredictable. So without revealing too much, we applied the same thinking to Harrison.
Exclusive: Kurtzman & Orci Talk Reveal Of ‘Into Darkness’ Villain Name