My understanding is there is no norm for APs as it really depends on your high school. Colleges look at the rigor of which courses you took and how many compared mainly to your high school as that is the main option you have.
Also, I do not think they highly value APs that kids self-study and do well on, instead want to see them take what is offered.
Agree on both counts- this is why schools limit the AP courses they offer, or have rules about how many APs kids can take at one time, or what year. Otherwise the competition would really be insane- I wish they had more limits at our school. As it was, DD did not take even the ‘standard’ number that many of her classmates did, because she wanted to continue with music, but she certainly felt at times that this might have put her at a disadvantage in comparison.
And there are certainly kids who go crazy with the self studying. It seems kind of like a summer job in some circles. But by my observations, it doesn’t seem to confer any advantage, at least from the admissions results, and one wonders if it actually backfires, as these kids tend not to be as involved in activities or the community- it just takes up so much of their time. And at least for us, in most cases the class was the point and where the learning happened, the exam and prep were for the most part an afterthought, though they obviously influenced the content and pace of the class.
I will say that one (questionably meaningful) advantage to having taken lots of APs is that at least for DD, the transition to college work was easy- she has much more free time and much more control of her time, and because of the brutal hs schedule, is excellent at time management.
With regards to GPA competition, I will just say that i think this is just as bad, if not worse than the AP stuff. Our school does not rank kids, to discourage competition, but they do reveal grade distribution. For last year’s graduating class, there were roughly 75 students, out of a total of about 350, who had GPAs of 97 or above. The actual numbers work out to above 20% of the class having an A+ or above average. That’s crazy- they all look the same on paper, all presumably have strong test scores. Hence the intense competition and extracurricular arms race, and the less-than-honest application mess.