One way to view the problem that Mutation Testing solves is, there's no test suite for the test suite. And so there's no safety net to enable refactoring the test code. It's test suites all the way down.
Mutation testing solves this infinite recursion problem by automating the test-suite-test-suite creation.
I have added it. It got removed for adding to the build time. Never really found many issues, so I couldn't argue to keep it. Did point out that the argument was essentially against testing.
So I actually break my application first to make the tests fail, and then refactor them while failing to ensure that they still fail. Finally, I undo my changes to the app code, and the tests should all pass again. I guess this is essentially a manually performed mutation test.