> If the districts are overrun with parents looking for advanced learning, why don't they offer it?

probably because a fair chunk of the kids aren't actually gifted, and if you cave to the parent's demands then you end up with a "if everyone is gifted, then no one is gifted" situation.

Our local school frequently mentions that their 50th percentile is at the level of the 75th percentile nationally, which indicates that a decent number of the students are in fact well above average.

That doesn't mean that the dilemma you mention wouldn't arise, but presumably there are objective tests that could be used to make determinations. It wouldn't be a panacea, but it would be better than ignoring advanced students like they're doing now.

Schools adjust their curriculums for the measured state of their student bodies. This is a major reason why they test and measure at the school level.

So if the school’s student body as whole outperforms the national average, then that school’s curriculum is enriched to meet the students where they are. State standards are a floor, not a ceiling.

This is good for the kids but not easily visible to the parents the way that placement in a gifted program is. Unfortunately, for families interested in markers of achievement, sometimes they will be unsatisfied with anything short of that letter that their child has been placed in the gifted program.

75th percentile is pretty mediocre when you realize how low the bar for the 50th percentile really is.

Thing is, when the mean is pushed out, the tail is pushed out too.

Sure but then isn't the outcome that the kid clearly struggles in the class and then drops back down? There's nothing wrong with that either.

There is if the parents make a big stink or if it hurts the students. Getting the students into the correct level class (in both directions!) is not entirely trivial.