This got a bit skewed during Covid, at least for us locally. Basically, AYSO was super liability-averse, and delayed restarting their program for about a year and a half after it was demonstrably "safe" to do so. This caused a lot of parents, myself included, who were looking for some way to keep their kids active in sports, to look at clubs, and the club registrations exploded as a result. See also the notes about AYSO suffering now, in part as a direct result of their actions a few years ago, when they prioritized their own liability paranoia over the well-being of the kids.
Our local club has never recruited from AYSO/rec, as far as I know; the exodus of kids to club was a self-inflicted wound from AYSO. It has only persisted and grown due to word of mouth, and bad feelings within this generation of parents toward AYSO, in my perception (it also didn't help that AYSO now requires 6+ different legal agreements just to sign up, and even more to volunteer, and has always treated parents like servants who should be grateful for any scraps, but while that is frustrating, I don't think it was the main factor here).