Briefly, the path to the championship works like this. After the regular college baseball season is over, 64 teams are selected to play in 16 regional double-elimination tournaments. The winners of these then play in one of eight "super regional" best-of-three tournaments. The eight winners of the super regionals head to the World Series where they are sorted into two four-team double-elimination "tournaments," and the two winners then play a best-of-three series for the championship.
The problem lies in the assumption that most of the time the winners of best-of-three series are the best team. Unfortunately, that isn't the case. Imagine, for the moment, that two teams are in a playoff, and one, the favorite will win 55% of the time (given enough games), while the other, the underdog, will win 45% of the time (again, given enough games). In such a scenario, in a three game series, the underdog will win the playoff 42.53% of the time. In a five game series, the underdog will win the playoff 40.69% of the time. And, in a seven game series, the underdog will win the playoff 39.17% of the time. And these probabilities don't even take into account the possibility that the favorites will suffer a key injury along the way. Thus, while the favorites will win playoff series of 3, 5, and 7 games more often than will the underdogs, underdogs will still win far more often than most people probably realize. My guess is that the likelihood that one of the underdogs will win a four-team, double-elimination tournaments is even higher.
In short, when teams have to win two best-of-three playoff series and two four-team, double-elimination tournaments in order to be crowned champion, there's a strong likelihood that the eventual champion isn't the best team in the country. Put differently, the probability that that best team will not win it all is far too high, which is why the College World Series isn't fair (at least if the goal is for the best team to be crowned champion).
What could be changed? At a minimum, I think that the NCAA give the top eight teams in the country a bye to the super regionals. It's not a perfect solution, but it would increase the likelihood that that best teams will at least reach the World Series. An even better scenario would be for the NCAA to give the top four teams a bye to the World Series. That almost certainly won't happen, but it would make things more fair.
Similar arguments could be made for the NBA, NHL, and MLB. Both the NBA and NHL require the top teams to play four rounds of playoffs. It makes for great TV, but it increases the likelihood that the better teams will be upset. Both leagues could improve matters if they gave the top two teams in each division a bye for the first round, and then let the next four teams battle it out for the other spots. This would reduce the number of teams making the playoffs from eight to six, but that would be more than acceptable if the goal is for the best team to win the championship (at least most of the time). Major League Baseball playoffs could give the top four teams in each league a bye, but as I noted some time ago, the one-game wild card is a terrible idea ("The Baseball Playoffs Need to Change"). A better approach would be for the top two teams in each league to receive a bye. Then, the other four teams could play best-of-seven series. Again, not ideal, but it would be more fair than it is right now.