I'd say the proportion of "unlikely patterns" in a private key of size n is more like very close to 0.00% (zero percent) the higher n gets. And it goes towards 0 really fast as n grows exponentially.

The amount of the sum of valid distinct combinations when selecting k elements, from a set of n, is massively larger towards the middle (n/2) and the close ranges around the middle, compared to the edges.

And this gap gets tighter and tighter as n increases, resembling a straight up point in the middle, which contains when looking at it with a "microscope" 99.9999% of all the possibilities. Everything else (the 0.00001%) is in the ranges before and after the central point.

This is called the central limit theorem (long-term, all results will be around the average). If this law would be invalid in observation, then it would mean randomness is not part of the structure of the game, and bias of the phenomenon (a fake coin, a compromised dice, non-random generated bits) can be proven with 99.99% certainty, But guess what, we have solutions already found with sequences of eleven consecutive 1 bits, and all the other sorts of sequences of 1 and 0 as well, which if you compute probabilistically, are not at all far away from the statistical model of a randomly generated phenomenon, so...? Excluding patterns just complicates the efficiency of the search, not sure I would play such a gamble (higher bid, lower reward).