I'm not sure where you got this idea of people being 24/7 on call for production. That's not a thing in the real world. We use rotas.

> come up with a process (QA) that finds these bugs before deployment or that allows you to roll back to a more stable version easily.

Aha! This magical process that mitigates deployment risks is also known as CI/CD. Which, it turns out, is usually used quite a lot in DevOps teams as it means each team member can see their code move from development all the way to production and fix problems as they appear. (hint: understanding this process is the "being responsible for your code in production" part).