Lets say you go moderately deep, and have a pressure differential of 10 atmospheres (say 11 atm on the outside, and 1 on the inside). The pressure differential causes water to be pumped into the container until there is no pressure difference and the water flow stops. To restore the pressure differential you need to pump the water out - so you'd need the pump to provide 10 atm of pressure to evacuate the chamber.
At that point, why not just have a pump here on the surface to provide the 10 atm of pressure and not deal with the hassle of pumping it up from under the ocean needlessly? You negate the energy gained from the ocean depths by bringing that water back up the surface.
This is magical thinking where you coast your bike down a 10 foot ramp and expect to go 20 feet up on the other side.