It is a strong disagree from me: end-to-end tests have always been fragile and slow, and feedback loop time is the boundary at which any coder (agentic or human) needs to operate on. If your agents need to wait 2h to see if their every change is valid, you'll be beat by humans doing properly structured "just enough" testing.
though I find in practice end to end tests are not that fragile. It took us a decade of effort to find and mitigate all the little issues that make them fragile though so perhaps you don't want to go that far. I wish I could make the end to end tests faster though, but fragile they are not.
I am not disagreeing most projects evolve test suites which have duplicated, useless tests as a majority. But it can be done better.
As part of the proper testing strategy, you will have tests that cover individual behavior of a small block/function (real "unit" tests), tests that cover integration points only up to the integration itself, and a small number of end-to-end or multi-component integration tests.
Only the last category should stay mostly idempotent under refactoring, depending on the type of refactor you are doing.
Integration tests will obviously be affected when you are refactoring the interfaces between components, and unit tests will be affected when you are refactoring the components themselves. Yes, you should apply the strategy that keeps it under incremental reverse TDD approach (do the refactor and keep the old interface, potentially by calling into new API from the old; then in second step replace use of old API as well, including in tests).
Tests generally define behavior and implementation in a TDD approach: it'd be weird if they do not need changing at all when you are changing the implementation.