Except that this isn't the case. We know empirically because we have enumerated the single precision space completely.

So, the problem isn't bounded by simple probabilities. There are other properties involved that cause it to diverge from the "naive" probabilistic estimates. What those properties are we don't know yet.

The "rounding" problem is called the "Table Maker's Dilemma" and it descends into some pretty fundamental transcendental number theory.

This is not an "easy" problem. Proof that PI was transcendental is relatively modern (1885).