Few students could get into every school, and not everyone should. Within any single school, few if any students could get into every class; again, not everyone should. So different institutions handle different sorts of students, or at least those who place differently–very much as you suggest, if I understand you.
To a large extent, this seems to be a good deal of what the community college system handles. Insofar as I have been privileged to see it, community colleges mostly handle nontraditional and remedial students better than do state colleges and universities. Class size is smaller, reduced costs allow students greater flexibility to feel a path through curricula with greater access to instructors. Instructors enjoy quite a bit more flexibility within administrative guidelines than do high school teachers. Many make good use of that, as high school teachers likely would were they granted it.
I suppose high schools with adult school courses could handle most of what community colleges do were they given the funding to do so. I am not sure that that’s what you are suggesting, though. If so, I am not sure of the advantage. The high schools have plenty to do as is, and this would require them to develop something like a community college system on top of what they have at present.
High schools also have considerable difficulties because they have to satisfy the parents of minor students. This leads to administrating towards liability control, usually at the expense of education. Then the centralized “educational reform” proffered by politicians generally amounts to removing or dumbing down any information not directly related to an employable task. Critical thinking gets skipped or repressed. That happens plenty in universities, too, but it is easier to find islands of greater creativity within the looser system.
Maybe there should be a very different high school setup that has these qualities. But I don’t think we should be testing people to see whether they should be educated, still less to see whether their schools should be funded. I think we should just test people to see how we might best help them be educated.