You can make sounds underwater on a breath of air... try it. The trouble is for humans is twofold:
1) getting a new breath of air while underwater, and
2) being intelligible.
The first problem has been solved by the excellent ability of the Air Genasi to never run out of breath.
Now while shouting at your buddy to get his attention so he can see the big flounder you poked a stick at is not generally a problem underwater, I would be hesitant to use the same method to invoke mystical words of power that called lightning from nothingness... (Also; If your doesn't know where you are, your buddy will have a difficult time locating you, as sound travels MUCH faster through water, removing the possibility of defining the direction of the sound.)
There are several problems when casting spells underwater. Spell components tend to get wet... Live spiders, bat guano and diamond dust tend to not take to water as some of our feathered friends. Not to mention the fact that touch spells may discharge immediately (sort of up to DM whim whether the water causes this or not).
I wouldn't allow the character to cast spells underwater unhindered. I would say they would be just as hindered as a human, as they must be able to pronounce the words correctly, something that the water distorts. But then I would not allow spell casting in conjunction with water breathing either.
It has nothing to do with vocal chords being used to being underwater. It is the sound itself which is distorted by the medium.
I guess I just miss the old spell airy water...