While there may not be a huge difference in a 6-6 versus a 5-7 season, bowl eligibility is college football's recognition for achievement.
Bowl eligibility boosts team morale, provides additional practice time, offers exposure on a national stage, and helps recruiting. Plus, it’s a great reward for the players and fans!
Regardless of whether we remember who played in which bowls, the extra game is not a small thing. For a graduating senior with no pro prospects, it's one more game on an elevated stage. While some players opt out, others use the bowl game as a final resume-building opportunity for a future pro career. For coaches and younger players, bowl games are great for development and improvement. It's another game - usually against a good opponent - and gives the additional practice time, which can be a tremendous advantage for development going into the next season.
Bowl games make a lot of money for the football teams and their conference and for the local communities in which they are played. They also make a lot of money for the media partners.
You may not get excited, but most fans want more football - and whether you attend and get to visit a fun destination city or just watch on TV - it's good, fun entertainment.
I suggest you stop thinking of them as meaningless exhibition games and embrace the post-season culture of college football.