Totally agree that automation will never fully replace the value of human-powered testing. (Though it is great for the rote regression-testing stuff. The "drudgery", as you put it.)
Isn't the problem with relying too much on unit and integration tests that they don't consider the end-to-end app experience? (Which, in my mind, is what ultimately matters when customers think of "quality".)
IMHO, yep - it's a balance, but the great thing is they can be quick to run, and run locally-easily; which is great for developers to get fast-feedback. Unit testing is unlikely to catch all end-user level issues though; traditional automation too, which is why human-testing is still valuable today.
Isn't the problem with relying too much on unit and integration tests that they don't consider the end-to-end app experience? (Which, in my mind, is what ultimately matters when customers think of "quality".)