Dance with four games?

Not all conferences allow all their teams to play in the conference tournament, but some do. Therefore, while not at all likely, it is entirely possible for a team not to win a game all season, but then win four (or however many) games in the tournament and be the conference's representative in the NCAA tournament. Then you would have a 4-25 team playing for the national championship. Now, really, do you think a team that bad deserves that honor? Obviously not. But that is how the system currently operates. Therefore, I conclude that the system is broken and needs to be fixed.