Yeah knockout matches are really good, much more intense cause if they lose they will get eliminated.
A very good question you asked I would say cause I never thought myself. Now I think, and conclude that, there are so many football teams, if some team get eliminate in first round they have to sit out whole year and do nothing. This format is not good as lot of talent will just go waste and the players won't be enthusiastic, they will not get more money and leave footballl eventually. People will stop supporting football(or their city team). In BPL knid of league, all teams get to play lot of matches. One important point is MONEY. The organizers of the competition are getting more money as they have to manage 20 teams(for example) and each team plays whole year(almost) so people are going to watch match every weekend.
Learned from ico -> After all this, someone thought why not let champions of each league play together? OK then lets organize, a tougher competition only for champions where they have to fight'till death(exaggerate)'. Later they modified some rules and kept UCL only for top leagues of few top European Countries(in football)
But I am not sure for all this. I just thought. Let someone with more knowledge comment on this.