Two major distinctions here:
1) The Joel is a basketball-oriented arena. It's old and in desperate need of updating, but still, it was at the 2007 game-which-should-not-be-named that I first said to myself, "this is what MU needs... a dedicated basketball arena."
2) Though on the outskirts & across University Pkwy, the Joel is still considered to be "on-campus" at WF.
In other words, I don't think MU would be keen on the idea of purchasing a multi-purpose arena that is a couple miles from campus... so a comparable option doesn't exist for MU. Though even if you could get around that, consider:
Auburn built their 9,000+ seat arena in 2011 for under $100M.
SLU built their 10,000+ seat arena in 2008 for $80M.
The City of Evansville built the 11,500-seat Ford Center in 2011 for $127M.
Nebraska will open their 16,000-seat publicly-funded wet dream this year at a cost of $180M+.
There's nothing like being at a college hoops game in a true basketball arena. If you've been to the Joyce, Pavillion, etc., you know what I'm talking about. The BC simply cannot duplicate that kind of atmosphere. Not to mention, I think something like that would drastically add to MU's "home-court advantage." I can't wait to watch MU play at Hinkle this year... despite Stevens' departure, that game should still be electric.
Assuming that MU could build a decent, 12,000 -14,000 seat basketball arena for $100-150M, I would rather MU commit that kind of money to building its own arena than spending even the $10-15M necessary just to renovate the BC. I wouldn't even take the Arena if they offered to give it away.