Why does pumped hydro require reservoirs for efficient energy storage? The problems with using pumped hydro as a long term battery are:

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*Hard to find locations physically suited for an extreme height gradient for two massive reservoirs (main issue).

*Water evaporates, so the locations also should be in cooler and rainy climates.

*Salt water used in the process was a problem, but a few test sites have proven this can be overcome.

So my question is about why the physics of a tall shaft in the ocean using pressure gradients rather than gravity isn't used. The math must not work out but I'm not really trained in physics, I wouldnt be able to work out the equations to know the answer.
Take this diagram, a very tall vertical pipe in the ocean:

To store energy, you spend it pumping water out of the top of the pipe.
To spend the stored energy, you:

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*open the bottom of the pipe allowing the huge pressure gradient at deep ocean levels push water inside and turn turbines.

*or, open the top and let the pressurte gradient / gravity push the water to the bottom.

Why wouldn't this work?
 A: There's a minor change which is needed to make it work.  You can't just pump water out of the top.  You need to pump it out of the bottom.  If you try to pump it out of the top, there's a maximum amount of water you can pump: 10.4m.  At that height, the negative pressure of your pump is sufficient to create a pure vacuum, boiling the water and creating cavitation.  10.4m is the highest column of water you can get by pumping it out from the top.  You can, however, exceed this by pumping from the bottom.  And, honestly, that's a more effective place anyways.  You already have turbines there, and most (all?) hydroelectric turbines can spin both directions.
The issue is a practical one: the structural integrity of the tube.  As you go down, the pressure increases rapidly.  This means you have to build the tube walls thicker as you go down.  Quickly what you find is that building the exact same structure on land, exposed to air pressure rather than water pressure, is vastly easier.
In the end, it all comes down to energy densities and costs.  Building the kind of structures which can store energy in this way is expensive, so we want to find cost effective methods.  For example, one of my favorites is where you connect two very large bladders (like an acre each) with a pump/generator, and pile a few meters of sand on top of one side.  You store energy by pumping into the resevoir covered in sand, lifting the sand.  You release it by pumping it the other way.  What makes this kind of approach desirable is that it is very cheap to move earth, compared to the cost of managing large tubes under the water.
And that says nothing of the effects of salt water.  Salt water is nasty stuff.  You really don't want to subject your turbines to it if you don't have to.  It can be done, and it does get done (especially for things like wave-power generators), but its expensive to maintain.
