I really like these questions! In the last year I've been working more on Django projects, where the default test is the integration test, and the best practice is the integration test backed by the same kind of database that is in production. Needless to say, when I join an existing Django project, I rarely encounter a unit test in its test suite.
I feel like these questions you pose might help in code review, or generally when talking about testing - maybe allow the person with an integration-centric view see the value of unit testing for themselves.