There are schools that use belts as a way to make additional money. In my opinion that is not a good practice. They charge inflating high fees for belts and testing. In my opinion there is no way to justify this. If it cost $20 to test for yellow belt it should be $20 to test for brown or black belt.
However, there are school to have ceremonies to go along with promotions. A portion of the fees goes towards the cost of the ceremony, certificate and registrations. This in my opinion is perfectly acceptable.
In our dojo we normally didn't charge for any testing. You only tested upon recommendations. However, there were a few cases that I witnessed that there was a $25 charge for a test. There was a student that wanted his black belt after years of study with us. He was moving out of state soon and desired to get the belt before he moved. He didn't have any recommendation, but really wanted to try to test. After a while my sensei said okay you can test because you are insisting, but you will have to pay a fee for the test. I don't believe you are ready. I won't test you. I will bring in some impartial instructors to test you. We will live with whatever they say. Regardless of pass or fail you have to pay the fee. He agreed and paid the fee. The fee went to the instructor from the outside dojo. I was his uke for the test. He failed the test. He was given more time to prepare before he could retest. He had to pay another fee and failed this test too with a different set of instructors. It was no fun being his uke. He had to defend against attacks from me. After my attacks he had to counter with a minimum amount of strikes, kicks, etc and he had to take me down to incapacitate me. This is where he struggled. It was hard for me too because I had to hit the floor for real. We didn't have any mats. I'm taking falls and he was lost on what to do. I tried to help him look good, but I couldn't tell him what to do. Because he was failing I didn't want to hit the floor anymore. I recall saying to myself I'm not going to be his uke again. I wasn't going to take this punishment if he is not ready to test. He went back and trained harder and bettered prepared himself. Months later he was tested again. Finally he passed. A few months later he moved from the Midwest to the East Coast to pursue his dream in acting. He has come back to visit and train.
That is a myth that white belts are worn without washing and that they eventually turn black because of dirt and oil. The culture of those raised in the Far East is that of a very traditional and clean. It would be considered disrespectful to come into the dojo with an unclean uniform. The obi is part of the uniform.
There are arts that only have white and black belts. There are some that have white, brown then black. The colored belt system was started by Dr. Jigoro Kano the founder of judo. It was used to show the progression of levels and learned techniques by its students (judoka). Others saw what was being done in judo and liked it. They decided to follow are create a similar system. later people began to add more belts, stripes, or tips to show progress and as a way to charge additional money.
I personally know one school that uses tips. They don't charge fr the tips. He uses it as a measurement to say that they completed a certain set of requirements. While I don't think all of that is necessary, it works in his dojo. He does charge fees for his testing. He has a commercial dojo and has to pay the rent.
I'm grateful that our dojo does not have that type of overhead.Therefore we don't have to charge for test or belts. We do not charge students to train with us. Many of our students wouldn't be able to afford to train inf there were monthly fees and dues. In the recent years our organization told my instructor that we must charge something for the test, especially since we don't charge for classes. So our test fee is $ 25. The student gets a brand new belt, patch and certificate of rank.
When I first began martial arts in 1982 we used to dye our belts after we got promoted. There was a small testing fee. I don't remember the cost. I paid for it myself by doing odd jobs like raking leaves, shoveling snow, planting gardens, grass, or other jobs like cleaning out people attacks. I also paid my own tournament fees, uniforms, and monthly dues.
In judo I went from:
white
yellow
orange
blue
brown
We got a certificate and a kyu rank patch.