Depends on the kind of tests. Old school "purist" unit tests are meant to help you verify the correctness of the code as you're writing it. Preventing regressions is better left to integration tests and E2E tests, or smoke tests. Alternatively to "unit tests" if your definition of "unit" is big enough (in which case it only works within the unit).
It's totally fine and common to write unit tests that are not meant to catch bugs of significant refactors. If you do it right, they should be so easy to author that throwing them away shouldn't matter.