This document has moved to: https://anthonysteele.github.io/PullRequestWorkflow
The git Pull Request is a powerful tool. But just because you have it, does not mean that you have to use it all the time.
I am thinking of a team that owns on a codebase and works on it regularly. Pull requests give outsiders a powerful thing that they did not have before: controlled access to apply changes that they need, with review by the owners. However it is not a good process to apply across the board to those same owners as a matter of course.
I always think of it as like a gate in an ancient walled city: A stranger can come in, if they pass inspection at the gate. Without the gate, they would be reduced to standing outside and shouting over the wall "We need this feature! And you need to update some urls!" and hope that it happens soon. So the gate allows them to come in and get business done, while respecting the local customs. But would you put that checkpoint inside the city and apply it to every citizen?
Pull request give review. There are other ways to do review. Human review is inconsistent, time-consuming, not scalable or repeatable and invariably has a political aspect. Review helps, but it is not a good substitute for e.g. simple test coverage.
Pull requests do not scale - you can wait for one PR to be merged before the next one, or you can anticipate trouble. They increase cycle time.
Continuous integration (CI) is the practice, in software engineering, of merging all developer working copies to a shared mainline several times a day. https://en.wikipedia.org/wiki/Continuous_integration
They encourage you to forget that the "Integration" in "Continuous Integration" literally means "Merge to master". A branch or PR is by defintion not integrated. You can test a PR, but you can't Continuously integrate it without closing it.
If I was starting from scratch with setting up a process, I would work hard to avoid mandatory Pull Requests and encourage Trunk-based development. It might be that the lack of PRs would force you to do other things: good, those other things are things worth having.