I take the bait
Belts are important in your gym and in your coache's eyes. His goal is to make you the best grappler you can be. Some coaches will put the focus on technique, others on the way you roll, some on competition results... Most of them will promote on the general way they behave and how their technique is applied in rolling. So the coach will use the belts to assess progress.
BJJ has the belt division to consider for competition. The coach wouldn't want to promote fast someone who is gonna get demolished in competition.
Now there's also natural talent to consider, physical abilities, strenght, coordination, grappling background, size...
We have guys that just use their size to beat up white belts and blue belts, they win a lot of rounds, smashing the guy, shoulder pressure in the neck in half guard or side control, managing to grind a kimura or americana. They rarely get promoted because they don't evolve, they are still easy to beat for the purple and brown belts because they don't use technique.
They can beat most blue belts, but they are still white belts, the coach want them to use technique, to find a way to get better against purple belts and brown belts, why would he promote a one trick poney.
Sure there's a limit, it would be stupid to promote a guy to purple belt that has trouble with 1 year white belts or every blue belts. But if a guy can do well with most people his size, why wouldn't he get promoted
Ergo rolling prowess aren't the only thing that matters for belt promotions.