Yep and if you're on-call for a week 24/7, I'd say it's only fair you do nothing else preemptively. Because you need to allow for the possibility of being paged.
No manager or employer would ever buy that shit because it rounds in the direction of less work though.
A shift pattern without anyone on call. 3x 8hr shifts in a 24hr day[1], optionally distributed around the planet so that all shifts are working in their local daytime.
The well-established solution to 24/7 availability is to operate a shift pattern.