I see two types of students.
Competitive and recreational.
When a student starts the coach decides if they are a competitive student or a recreational one. A recreational one may be a guy who isn't into sports. A middle aged person coming in after a long hiatus from physical activity, a girl just wanting to get self defense practice, or simply a guy with bigger priorities in his life than BJJ. Many of these people compete, and some of them win but they do not sacrifice their lives for BJJ. They don't think about cutting weight, and they don't spend extra hours at the gym doing drills or tournament strategies.
Than their are competitive students.
You know who these people are. A lot of them are students with lots of time and BJJ is a significant part of their life.
Now, competitive students and recreational students are held to different standards. If a competitive white has 3 tournies and comes in first in only two of them the coach may wait for the promotion. But a recreational white may do one tourny and come in at 3rd place, yet still get his promotion.
Is the recreational player better? No. The coach just has other plans for the competitive white. When mundials and pan ams come up, the competitive belts are there, not the recreational guys. That is what the coach is preparing their students for.
I could go through a recreational brown belt on aggression and speed alone, but that doesn't make me worthy of a brown belt, nor does it make the other guy weak. We are just in different categories and if you analyze your gym (not your college club) you will see it.
Competitive students win more matches than recreational ones, but if you ask them both to analyze a problem with someone's triangle choke or mount escape, you would find both answers just as technical.
Belts matter. Just not in the way everyone thinks.