I think human's attempts to make busy beavers may be clean, but chaos being hard to control doesn't matter to the "real" busy beavers because we pick from the entire range. I think that's one of the hardest things to wrap human brains around trying to intuit how the sequence behaves. We are selecting for the maximally pathological machines. If there is a frontier between chaos, order, and simply never halting, we are deliberately hunting the one that is just barely on that line. I don't think clean patterns can ever hope to compete with one that is exploiting chaos to just that bit that barely walks up to the line and doesn't quite, after a number of steps beyond any human ability to write down with any amount of notation we have, cross it.
> We are selecting for the maximally pathological machines.
This is not quite right. We're selecting for maximally long-running (or mark-producing, etc) programs. Whether those programs turn out to be "pathological" in some sense is an open question, and a question that can only be answered (to a limited extent) by observing and analyzing actual champion machines. Apriori, there's nothing we can say about what a champion program will do or what its code will be like. The Spaghetti Code Conjecture says that these champion programs will tend to be complicated. I have argued in the past that this may not be the case. It's entirely possible that the code of a champion program will be written more or less straightforwardly, and its long-running-ness comes from executing some bizarre and exotic mathematical function.
Actually, I think the more likely outcome is that some champions will be spaghetti and some will be clean. If they were all spaghetti or all clean, then that fact could be exploited to speed up the search process by discarding all programs not matching the property. And that sounds too good to be true, so it probably isn't. Maybe BB(8) champion is clean, BB(9) is spaghetti, etc, and there are no reliable trends.
But yeah, it's an opinion. :)