Division I-A college football also has a very unique history relative to those other levels. Until the 80s and 90s, people talked about how a national championship in college football was mythical (
Mythical national championship - Wikipedia). It wasn't necessarily something that was even strived for or on a team's radar. The game was, and still kind of is, a parochial game where rivalries and how you play in your conference are extremely important. They created these bowl games to "reward" teams for good seasons and pit conference champions against each other. A "national champion" was an odd concept in college football back in the day, just like it still is an odd concept in high school football today.
The bowls have been around for so long and are so entrenched in the economics and culture of the sport. It is only natural that as over time tastes changed and people wanted to declare a national champion, they build a playoff around the existing bowl structure.
I know this - the CFP is orders of magnitude better than the BCS, the BCS was orders of magnitude better than the Bowl Alliance/Bowl Coalition that preceded it, and that was better than the system that preceded it, which was nothing. This nostalgia for the BCS or old bowl systems is baffling to me. The reason the CFP was created was because of angst about the BCS.
Any sport is run by money. Nothing wrong with that. Believe me - if the NFL could adopt some alternative system for declaring a Super Bowl winner that would make them more money than a simple, single elimination tournament, they'd do it. I have no idea what such a system would be, because playoffs make all the sense in the world for pro sports leagues, but if one existed they'd make the switch.