Hosting of the Super Regional is a strong opportunity to advance (Arizona blew it a couple years ago). It is a system that works, while there are a limited number of teams that make it to the world series over the years, the mix is different every year.
Attendance is pretty much sold out for all the regionals and super regionals - the stadiums are small, some smaller than others. Neutral sites wouldn't work at all.
No, there isn't a lot of parity. Top half of the Big 12 and PAC, top third of the B1G, all the SEC, maybe 1/3 of the ACC plus select miscellaneous teams (often the same each year, such as ULL, James Madison, Fordham, DePaul, etc). Not so sure why the disparity - a lot of players out there. But, it is what it is.