What you usually want to limit isn't the number of threads but the number of threads doing a particular operation, such as accessing some service, so it's more

What you usually want to limit isn't the number of threads but the number of threads doing a particular operation, such as accessing some service, so it's more flexible (and efficient) to just guard that particular operation with a semaphore. The only place where you may want to limit the number of threads is at the entry to the system, but since the semaphore is the construct for limiting the number of anything, you might as well just use that there, too. For example, if the number of requests currently being processed is too high (above the semaphore's number of leases), you don't accept new connections.