Whether or not a club, gym or wellness center charges for facility usage (court time, time spent with punching bags, etc.) is an individual policy. Of those facilities that let members use various amenities freely, most do ask members to sign up in advance to reserve their time on the court, time with the bag, and so on.
The problem is, members often don't. If a facility doesn't have an associated cost for using that amenity, users assume it's not important to reserve in advance, and often bypass the sign-in sheet (or electronic sign-in program, if applicable). And of course, if there's no cost associated and no person waiting, it's not like they're doing anything wrong. Right?
Actually, that's wrong, and the fault is yours for not enforcing the policy. By not providing proper accounting for facilities in use, you're setting yourself up for trouble. If users come to you and want a place set aside for special programming (a new cycling studio, a place to do yoga), it's all too easy to just look at your sign-up sheets, see that the squash court or aerobics room isn't getting a lot of use, and put the wheels in motion to do away with it.
One of the gyms in my area recently moved to eliminate several racquetball courts, saying the space could be better used for something else, and that the courts weren't getting much traffic. Every time I'd seen them, they'd been busy with players, but the problem was that nobody bothered using the reservation sheets.
The racquetball players eventually won that argument, and the courts will stay as they are - for now. It took a petition, a lot of arguing and a public meeting in which one of the players described himself as "a polar bear on a shrinking iceberg," as poorly envisioned a metaphor as I've seen since the ice caps started melting. But it reiterated the importance of enforcing the reservation rule.
Putting the policy on the books isn't enough. Try asking people as they come in the door whether they're planning to use facilities, or have signed up in advance, either in-person, on the phone or online. Put up signs near the courts or punching bags, reminding people of the policy. Patrol the halls periodically and if necessary, interrupt people to let them know of the policy.
The paper trail needs to be alive and well. Start one now.