The reason why I mention decentralization is that the HS schedules are highly variable, depending on where you live. CA is one of only 5 or 6 states with Winter HS (the remainder are nearly equally split between Fall and Spring). It works for ECNL because the clubs schedule for all but the national events (showcases, playoffs). Then you have to factor, at least here in CA (not sure if other state federations have similar rules), CIF's rules on simultaneously playing HS and club. Set aside whether that might be too much, CIF is very, very against this and when I have communicated with them in the past (because a national team camp was not posted on the "approved" list that CIF posts (that permits participants' participation w/o losing eligibility), CIF officials were none too sympathetic to the individual player involved - they essentially said, "make a choice. And if your kid chooses camp over HS, it will give another player an opportunity on the HS squad). Last, you'd need some real coordination among schools/conferences/sections to have a routinized division of practice/game days - not every school has ample fields to just practice whenever and play games whenever (my kid goes to an urban school in the Bay Area; they have access to one field, there are 6 soccer teams (3 boys, 3 girls) for practice and games and there are other sports that use that same field while the HS I attended is suburban with ample space and about 1/3 the number of students).
I think national-level scheduling (like US Soccer does for DA) would be next to impossible in dealing with multiple state HS federations, multiple playing seasons, field availability issues, etc. Don't get me wrong - I really like your points from a theoretical standpoint but I'm not sure they can work from a practical one. I can't stand the prohibition on HS play b/c I think that the vast, vast majority of players (including those who play in college) won't sniff national team participation so is it really worth it to prohibit such a quintessential American experience as playing for your school? (I'm entire supportive of any player deciding she/he does not want to play HS but feel strongly it should be the player's decision, not the national governing body).