The math is simple: for example, in a 4096-bit search space, an h160 prefix is found on average once. If this were frequent (2 out of 3 prefixes in 4096 bits), the hash function would be broken. That's why this is a good guide for probabilistic searches. Anyone who says otherwise is wrong.
No, what's wrong is that you misinterpret the math and make some false statements. You are contradicting the very basis of actual theory of probabilities.
No, the hash function ain't broke if you find some prefix zero times, once, twice, or a hundred times (and it will happen if you keep trying, or else reality is broken, not the hash).
The often edge cases will eventually be counter-weighted by their opposite encounters (ranges with zero results).
You should straight up go to Princeton and give some lectures about this before they call the police.
Finding more than 1 (a prefix of length 3) in 4096 is rare, and omitting the target is even rarer. The length of the prefix doesn't matter as long as the block matches what's expected.
Nor do you try as much as you try, the probability will remain ≈ the same.
If finding more identical prefixes within 4096 were no longer so rare, the hashes would be broken.
You betray your intelligence in order to obscure ideas you don't share.