You could include basketball in that list as well. The only reason they mostly fly under the radar is the quantity of teams they let in. Even when basketball field was 64 teams, there was a lot of controversy as to who was left out because a lot of it was based on what the committee decided to look at that year. No one knows what that criterial was until after the committee maked their picks.
Overall hockey has the clearest/cleanest system. The formula says who is in and out. Everyone by know knows what is important to Pairwise. Beat the teams you should beat, win some of the games you shouldn't, and don't lose too many games. It helps a lot if your conference has a wining OOC record. Be high enough in the Pairwise rankings to outlast the autobids who are outside of the Pairwise top 16. If that doesn't work, win the conference tournament autobid. Which, IMO, is the best/only way to properly assess the change in a team's performance over time. How many teams have played themselves in/out based on their conference tournament performance? This keeps the human factor out of the selection, which as a CCHA fan, I appreciate.
Unless college hockey expands the the field to every team, no matter what criteria/formula is used there will never be a perfect selection formula/criteria. Even then people will complain with games that go to additional OTs and make their team "tired" for the the next game.