(not the OP but my 100 Croatian Lipa)Depends heavily on how stable app/system is.
I'm from PeopleSoft / ERP world. The same PeopleSoft HCM base application would generate one off-hours pager alert a month at one client; and half a dozen a night at another client; due to different customization/implementation/complexity of business logic and data.
Any on-call/on-shift rotation system must be viewed through the lens of actual demand and need.
At first client, we had 3-4 developers total who shared pagers on weekly basis, as per the OP, with no undue stress or impact on their day job.
At second client, we now have multi-tier support starting with on-shift (junior but specialized ops team members who stare at computer overnight and provide immediate response), Tier 1 and Tier 2 on-call support, and multi-level escalation rotation.
And yes, there are still people who get woken up all the time always, because buck eventually stops there :-/ . Being on call sucks, as per the title. I've been in 24x7 escalation roles; I don't drink to begin with so that's not an issue, but it absolutely had significant negative impact on my social & family life, sleep and stress levels. I've spent significant effort to a) Make the system better, both in terms of more reliable application, and deeper and more self-sufficient support team tree, and b) Move myself out of the role, though that relies on success in a).
I do find it fascinating to occasionally meet very senior people, with family and social life, who are positively EAGER to be on-call and engaged for every little thing all the time always - and then, unfortunately, have same expectations of literally everybody else ("Let's all come on bridge, always, for everything, anytime")