> Why do wireless APs constantly transmit (e.g., with a beacon interval of 10×/sec.), even when no devices are connected to them?
Just because an AP doesn't have any client devices associated to them, doesn't mean there are no client devices that would be "interested" in associating to them. In particular, this is useful in deployments that have multiple APs as this helps to provide information to clients so they can make decisions about roaming.
Additionally, beacon frames perform a number of different functions in addition to discovery. They serve as a timing source, provide other information to 802.11 devices, allow for power saving features in client devices, etc.