It’s hard to get math placement right. Like Choatiekid, my kid decided to take a lower level math than the actual placement Freshman year. Wanted to be sure to get the foundation part down. What happened was an easy year and solving things multiple ways. Kiddo doesn’t regret it as it was a bumpy year getting adjusted and honor math is honors math. Kid also knows that math is not the future path for him/her.
I think that many parents push their kids into levels where the kids might not fit. My kids have had to sit through many classes where Jane/Johnny was in the honors class and trying to keep up. In 90% of the cases, it was the parent pushing the kid. ( Not saying this is the case with OP, but it is a huge factor).
Sometimes the kid has the ability but doesn’t want to work and sometimes the kid doesn’t have the ability and the parent keeps pushing. Honestly, if the kid is breezing through the regular level they can jump into AP/Honors next year. I do sympathize with not be able to get into the class and still paying big $$.
There isn’t really an upside to getting into math beyond Calculus in high school. In fact, some schools don’t even have BC calc. IF a kid is going on to MIT/Caltech, they would be insane not to take the foundational courses and think their high school math is going to suffice. Math kids can take/make their own courses at many BS and that is great. If they are math kids they will find their niche by Junior/Senior year.
Our Freshman experience was many kids who were the “best” in their town could not keep up with the honors level. The kids were really stressed and most dropped down. Is there a possibility for OP’s kid to switch into the higher level course when someone else drops it? Change/add should be done soon.