The benefit is basically all the tests that you don't have to change and give you confidence that your refactorings don't break certain things.
But the drawback is all those tests that do need to be rewritten because of the refactoring, and so will slow you down again.
But in the end for this use-case, I think it's a good ROI. Probably the best use-case for TDD.
Look at the concept of sociable tests.
https://martinfowler.com/bliki/UnitTest.html
The benefit is basically all the tests that you don't have to change and give you confidence that your refactorings don't break certain things.
But the drawback is all those tests that do need to be rewritten because of the refactoring, and so will slow you down again.
But in the end for this use-case, I think it's a good ROI. Probably the best use-case for TDD.