There's no reason not to have multiple fail-safes. Receiving the alert on a device at 3am would still mean he could free up 8gb immediately and have breathing room to solve the problem. And remember this is for a single admin. Asking such a person to be on call 24-7 all year, vacations, holidays, weekends... Having a quick way to get breathing room can significantly reduce the stress & cognitive load of worrying about such things in your off-time.