Super common! I often tell My subs with their own devices to put them on right before we play and then I let them out at the end of the session. The only problem is- its hard to do a lot of cbt with the cage on; you definitely can't do ballbusting with a device on, you risk injury to yourself and the Domme's foot. Depending on the device and the sub's anatomy, it can be hard or impossible to use a vice or a parachute while also in a chastity cage.