Again, where are these schools?
At my TKD school we offer a product. A structured curriculum that goes step by step from white through black belt. We're upfront from the beginning that testing between belt levels is part of what we do.
The yellow belts works drills for basic sparring combinations while the blue or red belts do more advanced kicking drills etc. Higher belt curriculum is designed to build on the lessons from previous levels. There are legitimate reasons for this, (safety being primary).
Just like it's probably a bad idea to teach rubber guard and the twister to a brand new BJJ student... a jumping spinning kick is just going to injure an inexperienced kicker if they haven't learned correct body alignment and trained their muscles for balistic movements.
I have no doubt they exist as you say... but I've never seen a school (that uses a belt system) where they say that following the curriculum as layed out is optional. Testing to achieve the next level is part of the experience we provide. No one takes every test... only the ones they are ready and sign up for. If that takes 2 months or 2 years to go between belts it doesn't matter. Everyone's pace is their own.
A visitor is a separate issue; but if someone is joining to be a student... then they're joining to learn things the way we teach them. Someone who refused to test, but kept showing up for class (of course I've never seen it happen) would likely get bored of the same kata, basic drills, and line work eventually.
If people come wanting to dictate how they will be taught... well 'don't let the door hit ya where the good lord split ya'.
I feel its heavily implied for the ones i have experienced. Granted i have congeled some other things in there, Lau Gar for example has belt locks for courses, but i dont know how they word it personally. (and the mc dojo probbly does this by default anyway, as its to milk money out of you, well so are other martial arts orgs but another day)
the point is not "what belts exist for" its, you need X belt to do X course, they have otherwise made it sound like you can get fully access without grading.
I feel that they do/the blur the line and heavily imply it if not say that its optional a bit too much. this is also congealed with what i wrote above about the contradictory statement rant.
"A visitor is a separate issue; but if someone is joining to be a student... then they're joining to learn things the way we teach them. Someone who refused to test, but kept showing up for class (of course I've never seen it happen) would likely get bored of the same kata, basic drills, and line work eventually."
This is my point, they are strong armed INTO doing it. Unless you award them a honary belt their belt rank says "they can only do these forms" That would be strong arming to me, you join dont care much for belts, and then you get locked because of it. (then somone moans at you because you disliek TKD because of this, because apparntly its not a apt reason to dislike it)
My example would be one, i can do the 4d's good enough, so its a bland pointless pattern, i belive the only reason i got flagged that one time was because only 3 people turned up. (very much an exeption) i have also messaged some other people and they say they would or consider going as far to teach the next belt on request outside of a actual grading. ie if i wanted to learn something in yellow tag/belt, they would consider it if i was a white belt, and before i graded for the tag. Obviously more exeptions.
but i doubt they would without giving a honary belt to the person, teach them more than 1-2 ranks above themselves,and then its meaningless as they wont be able to access the orginisations courses etc if the school is part of a greater network, and if only one teacher has that agreement with you, the others may default you back. Pending on org as well, grading works diffrent, i know a krav maga orginisation lets the individual school grade some ranks, then the organisation itself has to grade the others.
an honary rank would be, you only offically have a yellow belt, but work and are treated as a red belt in your orginisation. a large part of my issue is the fact some make it out as "optional" or imply it honestly.
Addendum: If i join a sports TKD school to do the sport of it or to spar and patterns arent important[to me], patterns tend to be a large part of all TKD schools, sparring tends to take a lesser part, so if i dont want to grade, im going to get bored paying the person to do the same 4 things every day for questionable reasons. Where as in places no belts exist or no clear markers its more fluid. If you compare the two, the unranked one is a better fit for the state school comparision and anaology, the ranked one is not as it doesnt act the same.
there is a very distinct diffrence, you sadly cant have the pros of belts without cons and vice versa.
Last point: you provide the service of providing what ever martial art, combat sport etc you claim to do. that also requires honesty about what it is, what its scope and purpose is and how your orginsiation operates. the person also pays you to learn in part what they want/can do/are looking for, if they cant kick its pointless to teach them kicking for example. Its like if you paid a personal trainer, and they knew you couldnt do pushups, so decided to have you only do them for the full session isntead of building up your ability with easier exercises to a pushup. (pet peeve) your going to stop paying them by the way.
Hell, i have heard of some japanese schools having some westerners sit aside to "test their patience" god i hope they didnt pay for that, i wouldnt pay for that. and its fully understandable not to or to remain there from that. Tangents aside, hopefully that actually replied to something.
Addendum: I am pretty biased against TKD honestly and thats the only one i have experinced so keep that in note. But i can articulate all of my exomplaints about it and they seem to hold water. (at least some in part)
Addendum 2: This subject still continues to confuse and annoy me with the amount of contradictory statements in the overall community, i cant think of something as fractured as martial arts honestly.
Addendum 3: I wrote the orginal reply probbly without sufficent sleep to write it.