The best way to manage on-call is to not have on-call. On-call means the organization is understaffed. Hiring new positions to handle off hours, will solve the problem. Good luck.
If you’re in a “boring” industry, it’s completely infeasible to hire a 24/7 dev team just to cover on-call. Doubly so if on-call requires physical access or security clearance.
If you’re at some multinational big tech firm, sure, I can see how it makes sense to geographically distribute the team so that there’s no “out of hours” support. For the rest of the industry it’s a non-starter.
They are not "no-call" they are the night shift.
Have a mature enough development process and pipeline that production deployments are repeatable and predictable at any time.
Bake testing into the procedure.