To answer your last question, if the school is affiliated with a larger organization, such as ATA, ITF, or KKW, a portion of the fee goes to the organization. This is reasonable; administrative work and record keeping on the part of the organization provides the student with benefits and doesn't get done by itself.I've read a lot of (valid) complaints about Mcdojos and such, and how people may be lead to expect to advance to the next level because they're paying for a belt test. Well here's a thought: what if the instructors eliminated testing fees altogether?
Yes I do know of at least one case where this happened. Every few months there were scheduled testing dates that would be posted ahead of time to give students a deadline to work toward. The students would acquire their own belts ahead of time and bring them to the test. When testing was over, if they passed, the instructor would then present their belts formally. If not, they were encouraged to continue training as usual, and later, when the instructor felt they earned it, he would present their belt to them formally at the beginning of the next regularly scheduled class time.
Sometimes this instructor would feel that a student had progressed and deserved to be promoted, but there was no upcoming scheduled test date in the near future, so he would say "go buy your next belt and bring it to the next class" and he would formally present it then.
Certificates were printed and presented later upon request. A lot of people couldn't care less about getting their certificates and so never asked for them.
Nobody was ever charged for testing or certificates. The instructor was never under pressure from parents or adult students to promote a student because they had "paid for it".
Truthfully, I think that it should be this way everywhere. Why isn't it?
Now, if the school is nonaffiliated, then the system that you describe works just fine; no need to pay administrative costs when there's no administration to pay.
Personally, I think that the costs of the actual belts and certificates should simply be factored into the fees that the student pays or have the student pay the fee for the belt and cert, rather than making them go chase it down. Given what the belt and a paper certificate costs, monthly fees would only be altered by five dollars or less.
Daniel