If yours is a highly resourced high school (let’s say offering 20+ AP classes) and you take only 2-4 of them, then yes, AO’s at top colleges take that into account and ding you for it. But that doesn’t seem to be the case for your child.
“AP maxxing” once you get beyond a certain number doesn’t help you. If the top kids in such a highly resourced high school typically take 8-12 AP’s, then someone taking 16 AP’s isn’t better off. AO’s will often say “8-12 is good enough to show academic rigor” and they move on to other evaluation criteria like letters of recommendation or EC’s or essays.