Probably because I’m old, I’ve seen a number of variations of this at clubs where I’ve been a member.
For many years, I was a member of a club that didn’t allow walking on weekend mornings.
Then I was a member at a club that allowed walking anytime, but if you wanted to use a push cart, you had to rent one from the club; the club’s carts were black Sun Mountain speed carts, and I owned a black Sun Mountain speed cart, which I couldn’t use.
Next, I was at a club that allowed walking anytime, but charged a $4 “trail fee” for walking on weekend mornings, but only during Daylight Savings.
I never really had a problem with any of these because the GMs made it clear when we discussed it that this was a revenue issue; it wasn’t about pace of play, or uniformity, or anti-walking, or anything else. It was just dollars; all were very affordable clubs, and I understood.
Now I’m a member at a much more expensive club; walking anytime, and you can use your own push cart. I have an electric trolley, which I pay the club $225/year to store. Ironically, I spend MUCH more per year now than I ever did at any of the other clubs. And that’s ok, too.