Should we have net positive code coverage diff requirement on PRs?

[banesullivan]

Should we implement a hard CI check that requires a net positive code coverage on the diff? This would help ensure we are writing decent tests but I could also see it being a bit of a nuisance

[MatthewFlamm]

I think it should be implemented, but ignored when it makes sense. For example, a style-only change that touches several modules should not be required to have net positive code coverage, but new feature additions should.