If your product consists of somewhat reusable libraries that you compose together, and extend when needed, having strong unit tests for the low level functionality helps immensely when it comes time to refactor. You know, stuff like "when given int(2) and int(3) as arguments, add(int, int) returns int(5)".
Likewise those high level API tests that ensure the system-as-a-whole is still doing approximately what it's supposed to, regardless of what mess of wires and small aliens is inside the black box are super useful for moving forward as both proof of functionality and guard against regression.
It's the stuff in the middle that's icky IMO. Integration tests that are testing your glue that, especially these days with clouds, containers, microservices etc, can be quite far removed from any codebases you might maintain. I don't have a good solution for it, but I'm searchin'...