Isn’t this the way everyone works? Write code, run some tests/linting locally, then create a PR to master and the CI server runs all the tests and reports pass/fail. Changes without a pass can’t be merged to master.
My issue with this approach is that it becomes tricky to scale since you can only have one job running at a time. Allowing master to potentially break scales better because you can run a job for each commit on master which hasn't been evaluated. Technically you could make that approach work by instead of rebasing onto master rebasing onto the last commit that is being tested, but this adds extra complexity which I don't think standard tooling can easily handle.
https://zuul-ci.org/ and some other systems solve it by optimistic merges. If there's already a merge job running, the next one assumes that will succeed. And tests on merged master + first change + itself. If anything breaks, the optimistic merges are dropped from the queue and everything starts from the second chance only. Openstack uses it and it works pretty well if the merges typically don't fail.
The solution is to require that all PR must be rebased/synced to master before they can be merged. GitHub has an option for enforcing this. The downside is that this often results in lots of re-running of tests.