And, winning A is a big deal to the less competitive teams. As for why this system exists, it's deference to the reality that, say, Farmington (don't know if they're typically A or AA*) isn't in real competition with Stevenson. After all, if not for this system, all but, say, 12-15 teams wouldn't have much reason to go downstate (upstate if you're in the Saint Louis suburbs) in the first place given the sheer competitive level there.
*As a side remark, an interesting consequence of the criteria used to place teams in divisions has tragic consequences for those teams that win easier Regionals (southern, western, Rockford, maybe CPS?) because they've landed in AA before with no real reason to be there other than getting first in their (easier) region. Anyway, it's not a perfect system but gets the job done.