The best argument that I can come up with for having a tournament for a league like the SEC is that just having the prospect of making the tournament helps keep teams playing to win up until the end. Without a tournament to play for, teams that aren't going to get an at large bid might decide to play for experience rather than playing to win the last three or four weeks, and that could affect who wins the championship (if one of the leaders faces such a team in the final stretch, when they have noting to play for).
I'd rather go to pool play. Yes, it is a contrived way to decide an auto bid, but it provides a decent fan experience while not taxing the pitching staffs.