That would work only if the fresh water is enclosed in some kind of container, like a plastic bag, otherwise it will mix with the salt water before reaching the surface.

Perhaps the difference in weight between 2 columns of water of equal height, but where one of the columns is of fresh water and the other of salt water, which causes a difference in pressure at their bases, can be exploited somehow for pumping the fresh water, i.e. for pushing it inside a pipe towards the surface, but with some kind of piston that separates it from the salt water.

It shouldn't be too difficult to fill up a balloon like container at the bottom of the sea with fresh water. Once the container is filled it will float up to the surface.

The container doesn't need to be super engineered, since it is filled with water so there is no pressure difference between the inside and outside.

If you have balloon-like containers instead of a pipe, then you expend energy to submerge replacement containers down to the depth at which desalination happens.

You can just have the container be slightly more dense than water and it will just sink.

I guess many people have not been scuba diving since these concepts seem so foreign to them.

So then you need to fill the containers with something more dense, in which case you need to expend energy bringing that to the middle of the ocean where this whole contraption is going to be. You also need a way of expelling it from the container so that it can be replaced by freshwater, and then you have pollution concerns since it will sink to the bottom of the ocean, where it will pile up over time.

The container collapses onto itself. You can for example Google a hydration bladder to get the idea. At the surface you just squeeze the container flat to remove all the freshwater and then it will sink on its own.