That's because you don't really need 32 bits for storing the depth, and only the depth buffer allows you to have 16 bit values.
To do so I had to tweak a few things, for example I needed to remap the distance between fragment and light to the interval [0;1], because the depth buffer can only accept those buffers.
In the end everything was unexpectedly working in less then an hour, which is a relief after the last week. Now I'll stop working on point light shadows, and probably I will add spotlights (with the relative shadows), and then stop working on graphic stuff for a while, and move to other aspects of the engine.
In the picture I have 9 dynamic lights (10 with the directional light) casting lots of shadows from 121 parallelepipeds. It runs at 50 fps, which is quite good on my card I guess, considering that each light requires 6 renderings.
I doesn't surprise me that even in modern games there are just a few lights on screen in the same moment, and not all of them are shadow casting.
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