AB may be less demanding than BC, but adcoms aren’t going to roll their eyes and say he cheated rigor. Not as a 10th grader. If the hs allows, let him take BC later or a more demanding math at the local comm college.
Yes, a B can hurt. There’s the reality of the fierce competition for STEM at top colleges versus anecdotal info. (And remember, our own college experiences were ages ago.)
Add other factors, like geo diversity. If you come from an area strong in STEM applicants, it’s that much tougher competition. Bear in mind also that, in the end, getting into a holistic elite is more than your academic record and stats.