Regular public schools are limited to the curriculum prescribed by their school boards and generally can't deviate or experiment much. They're also, by definition, limited to students in a specific geographical area rather than any selection criteria. As others have noted, this goes both ways - charter/magnet schools can choose to serve the highest aptitude students (as most do), but they can also choose to serve at-risk or academically challenged students as this one does.

So why can’t school boards prescribe such things? The geo limit doesn’t matter much/at all.

No explicit reason, they just generally don't. When you're beholden to voters or a city council, your job is least threatened when you don't rock the boat. If you do rock it, you better make sure you're right or it's not likely to end well for you. Meanwhile, your 'subjects' are unwitting participants who thought they'd be getting a normal education, not early adopters explicitly willing to try something new. All of these factors discourage experimentation.

Non-charter/magnet publicly funded schools cannot select/reject children based on their demographics or aptitude. The most they can do is have a preference based on locality or the presence of a sibling in the school - which can and does introduce its own selection bias.

Ultimately, the public school system has to serve students who have been excluded from more selective schools, otherwise you end up as a society where the most basic education is a privilege instead of a right.

I don’t see how that prevents them from improving education.

If you can select students who come from more better environments (magnet/charter schools), you don't need to spend a considerable amount of resources to manage/treat the social issues that accompany students from worse environments. The latter is what public schools that serve poorer communities have to deal with.