In addition to my own BJJ/JKD/MMA gym, I've worked as a professional ballroom dancer and studio manager in multiple locations.
Some of those places don't want to give rates over the phone, because the sticker shock can send people running - we're talking over $100 per 45 minute private lesson, and in most cases you're taking a minimum of one of these per week. Some people see the prices and take off running, but plenty of others are fine with it and sign up. I had one client who took six lessons with me every week.
Some studios had no problem answering the question over the phone - if you asked, they'd give you the number with no evasion. Their rationale was that they were gonna see the prices eventually, and if that was enough to make them faint, let's save everyone the hassle of doing it in person. But there's a vast middle ground of potential client who could afford the rates if they really thought it was worthwhile, and those are the people that you want to have come down, see the value offered, and make the decision with a full appreciation for what they're receiving.
Before all this, at my gym, I posted the rates for a long time. I thought it made me competitive, because my rates were in the middle for my area. I learned later that my rates were actually on the low side compared to my competition. But many, many people wanted to haggle and get free training (I learned later that this is a sign you're on the discount-end of the pricing spectrum). Eventually I raised my rates and took them off the website. I thought people would raise hell, but actually enrollment improved substantially. We had more people come down to check it out, and very little pushback when they learned the prices.
Nowadays when I worry that BJJ costs too much, I like to remind myself just how many clients I had at the dance studio, and how many lessons per week they took My six-privates-per-week client was an outlier, but I had plenty of people taking 2-3 per week. These clients were paying $800-1200 per month on lessons (to say nothing of gear, studio swag, and special events). And the primary studio was just a mile from where my BJJ gym was - so it's not like this was a different population.
I say all that to say - clients have their own expectation built up for what a thing should cost and what they will get for their money. Sometimes these track reality and sometimes they don't. (Studio owners also have their own assumptions about these, and they're often mistaken.) It can be very difficult to know whether to tell people the rates up front, because you don't know what a person thinks about those rates. You might miss out on plenty of good students who would actually pay what you're asking, if only they could experience the gym first. Knowing when to qualify and disqualify clients is a very tricky business with no right answer.