Well, it seems kind of difficult, in fact I am surprised it works. As you go deeper and deeper the water gets denser and denser which means the buoyant force becomes greater, which means that you have to exert a greater force to keep going down. If you rely purely on wings to exert that force, you will have to move with a pretty high velocity in order to exert sufficient force. It seems much simpler to just take on ballast and rely on good old gravity to pull you down.
If this thing works at all, my guess is it will have to go pretty fast, which would make it kind of dangerous and kind of hard to do exploration with.
Water does not get significantly more dense under pressure. According to Wikipedia, at an ocean depth of 4km, its volume is reduced by only 1.8%. That's not going to have to have much effect on the speed required to get lift.
If this thing works at all, my guess is it will have to go pretty fast, which would make it kind of dangerous and kind of hard to do exploration with.