Depends on the school district and size of the school. For example, Texas high schools are for the most part huge and can accommodate anyone who wants to take AP classes without question. We did check with our counselor but they were more than happy students took AP classes.
It wasn't a size thing as much as for "protecting" students from classes they couldn't really handle. I can't speak to whether that was necessary or not; it's always worked out very well for me to try things that I didn't think I could achieve, but maybe that doesn't generalize to everyone.
