@mathyone: I’ll illustrate with an example then.
We’re talking about a high-performing school since the students may take as many as 10-12 AP classes or perhaps even more. Those tend to be in densely populated areas, wealthy areas, college towns (and/or) so access to resources isn’t an issue (transportation can be but not often). We’re not talking low-performing, rural, or inner city.
Think of three students, all of whom have an A average and purport to love math (or foreign language).
Student 1 has taken AP calc or AP foreign language as a sophomore, then nothing for two years, plus Ap Human Geo, AP Lang, APUSH, AP Stats, APES, AP Chem, AP Bio, AP Physics, AP Psychology, AP Gov, Ap Macro.
Student 2 has taken AP Calc or Ap foreign language as a sophomore, plus AP Lang, APUSH, AP Chem, and two DE semesters of college math/foreign language.
Student 3 has taken AP Calc or AP Foreign Language as a sophomore, only Honors classes in other areas, and has progressed 4 college levels beside AP Calc or AP Foreign Language.
I absolutely maintain that students 2 and 3 have better odds of admission at competitive colleges than student 1.
Collecting all the AP’s at your school causes un-necessary stress. There is no need ever to take 12 APs or to wonder if it’s enough; when if students skip lots of levels by taking classes over the summer, then stop taking classes in that subject, yes it’ll be detrimental.
If we’re talking highly gifted and highly motivated students, they will try to continue in their subject even if they exhaust their high school’s offerings. Even if nothing comes to fruition, they have tried different venues that may be mentioned in essays, additional information, or LORs. That thirst for knowledge is something that matters a lot to universities.