The reason the prices can't be quoted isn't to prevent people from budgeting. I could go into the fact that most people's true budget is much higher than they might initially think, but that is another can of worms so I will just simply set it aside at this point. For the sake of this argument here, I will simply accept that a person's initially quoted budget is all that he can possibly afford.
Here is what happens in reality:
People are usually scared to check out a gym in the first place, so they won't go check out two schools that are within budget. Say a person's budget is $150. Three schools are $175, $150, $100.
You are saying that this person should rule out $175 because it is not affordable. Then that person should check out $150 and $100 because they are. That would make sense, but it is not how people act in reality.
What I am saying is that this person will in reality just go straight to the $100 place, not even bother with the other two, and think that he saved $50-$75 when really he might be training at a more substandard place. The empirical fact is that most people operate this way, and it can be easily proven if you are a school owner who actually keeps track of these stats month by month.
Most of the people arguing for prices to be posted have never actually looked at the empirical data as a school owner. Try it sometime. Post your prices that are higher than your immediate competitors straight up and see how many potential students you convert to signed up students. Do that for six months and track it. Then take your prices down and do that for another six months. Track that number too. Try to keep the other variables the same.
If people acted rationally like the price posting proponents claim, the numbers should be about the same. Your price quote over the phone should only rule out people who truly cannot afford it no matter what. Those people would never sign up anyway since it is completely unaffordable, so even if they came in for a free trial without prices posted they would not convert to signed up students. You may have a lower conversion percentage, but the absolute numbers should be comparable.
Of course, I can tell you from personal empirical experience that these numbers will not be the same. People do not act rationally this way as a whole. You will have significantly less students signing up if you post the prices straight up. Potential students will jump straight to the lowest priced place and not even bother trying you out.
Regardless of how you theorize how people investigating schools should behave, they behave in the very predictable, empirically measurable way I have described. I have seen it happen again and again across multiple schools. It is just how it is. Trying to rationalize otherwise is like arguing that heavier things should fall faster. No matter how much sense that seems to make theoretically, it is empirically proven by the laws of physics to not be the case.
The challenge is to try it both ways and actually measure the results. You will see that not posting the prices gets you significantly more students signing up. That directly contradicts the fact that potential students are able to, on the whole, evaluate gyms fairly when given the prices up front. Their evaluation method changes dramatically if they try it first. It is not a budget thing.
