Problem is, that you might have to move the table legs through the floor to archive the desired result

I’ve done this with my dinner table several times.

I don’t think that’s exactly right. to create a plane you only need 3 points and 4th point can be on a different height than that plane. A different thing is when the ground itself is uneven and you manage to make both fit to the same shape.

There’s no guarantee you can draw a circle through the bottom of the four legs of a table (opposite legs can be off in the same direction). Also, most floors are not perfectly flat, therefore you can’t assume the floor is at one elevation.

Is there mathematical proof for this? It sounds like it could be true, but also sounds like you could actively create a floor which it wasn’t true for

This requires the legs to be all the same height and the floor to cause the wobble. That doesn’t happen often irl, but I’ve done it a few times and it always makes me happy when it works