Every kid is different and every HS is different, so there is no universal answer. Our local public HS offers more than 20 AP classes, the more serious students gravitate to those and the school regularly produces one or both of our state’s “State AP Scholar” award winners. I expect a student at this HS would need 12 or so APs to get the “most rigorous” designation on their counselor’s recommendation.
It irritates me when people denigrate those who choose to take a lot of APs. Yes, it’s true that it isn’t the case that “the most APs wins”, but for a kid to take a full complement of math/science APs, or the full course of history APs, or both, is a good thing. And it doesn’t necesarily make the kid a “textureless grind”.