A lot of instructors push this idea as well, sometimes directed at the parents.
It's part business, if they can convince them they have to "Stick it out to the end" that means more money for the school. Black belt clubs, big banners saying "We are a Black Belt school" and other such things reinforce this.
And, let's be honest, for many people it is the end. Even for those that continue to "train." The intensity drops, less training, more teaching kicks in. And yes, skills sometimes diminish and the belts seem shorter when tied.
It also matches other lessons / classes mentallity. In swimming lessons, you finish the last level and you're "done" unless you decide to pursue lifeguarding or teaching. In school you finish the last grade and you are "done" unless you decide to pursue a higher level. I think some people just view martial arts in the same way, that if you stop before black belt its the same as quitting school before you graduate.... and then there are of course schools that promote black belts using a "Graduation ceremony" and refer to it as such...
Andrew very well put my good man, too many people quit training and start teaching. I.E. the BB graduation is just ridiculous inmy eye anyway.
The best line is when you tie your belt it is getting shorter