Certainly a lot of things could be tested more; this would help.
But also, we might want to set Github to require the tests to pass on a PR before letting it be merged. I could be wrong, but I think a PR can be merged even if the tests fail.
This is a slight step away from "anyone can commit anything", I acknowledge. But it's also a step towards stability. At least the person would have to fix or delete the failing tests before merging.