There are many issues with being on-call, particularly in environments where false alerts routinely happen, and where management aren't in the rota so don't directly feel the pain. One of my biggest though is the concept of a weekly rota, with people being on-call for a full week at a time.

Sometimes that works fine, and you'll get no alerts all week, but incidents tend to cluster. If something has changed that caused an incident odds are it's going to have knock on effects, and you'll see more alarms over the course of a week. With a weekly rota you end up with one person handling that, who by the end of the week is completely destroyed.

Anywhere I've been responsible for setting up an on-call rota I've instead gone for daily rotations. That means if you were up in the night last night, someone else is going to be in the night tonight. It also means if nothing happens you don't have to spend an entire week either cancelling plans or lugging a laptop around with you just in case.