The solution to get paged at off hours a lot is rarely to hire additional teams to cover those times for you, at least not long term. For things you can control, you should fix the root causes of those issues. For things you can't control you should spend effort on making them within your control (eg architecture improvement). This takes time, so follow-the-sun rotation might be a stop gap solution, but you need to make sure it doesn't cover over the real problems without them getting any better.
From experience, it's really hard to fix the root causes of issues when you were woken up three times the night before and had two more of the same incident occur during the workday. In my case I struggled along for a couple years but the best thing to do was just leave and let it be someone else's problem.
If they cared about that they would either pay me so much money I'd be insane to walk away or they would hire people in other time zones to cover the load. Instead they chose to pay for their customer satisfaction with my burnout. The thing about that strategy is... eventually the thing holding their customer satisfaction together gets burnt out. So I leave. And even then they're still getting the better half of the bargain.
Sorry, I accidentally said you did the wrong thing for leaving. That wasn't my intention. Of course, leaving was the right choice for you.
What I meant was the company you were working for does not get the best quality or customer satisfaction by overworking you to the point where you have to leave. It would have been better for their software quality to handle things differently.
