Our public school does not allow subject acceleration because the grades don't teach the same subjects at the same time, they don't require the same number of minute of a subject for different grades, differentiation happens in the classroom, blah, blah, blah, blah, blah...

You've got a long way to go, but the closest thing we have to subject acceleration happens in middle school, where some kids will take 6th grade math, some will take take pre algebra, and some will take algebra.