One of the things I don't like is that not every team fully controls its own destiny at the start of the season. There are at least a few plausible scenarios where a team can win all its games and still not get in.
I also think, as a general rule, playoffs should be as big and inclusive as possible. I don't think there's anything to lose by including more at-large teams and more games. But there's quite a bit to gain, IMO.