In practice e2e tests don't cover all code paths and raise a question: what is the point? There is a code path explosion when going from a unit to an endpoint. A more low-level test can cover all code paths of every small unit, whereas tests at service boundary do not in practice do that. Even if they did, there would be a lot of duplication because different service endpoints would reuse the same units. Thus, I find e2e tests very limited in usability. They can demonstrate that the whole stack works together on a happy path, but that's about it.

You are testing that the software works. I think that is higher value than testing all possible code paths in isolation, and then still not having the guarantee that it all works.

The problem tends to be that programs most often break at the integration boundaries, though.