There will never be a way to test everything in an automated fashion. For those you can either have your expensive software engineers to painstakingly run very scenario regarding a change, or have a less expensive QA person do this. I guess it's management's call, but for large, complex systems it can take days to go through the scenarios for some some bug fixes - and those are days not spent fixing other bugs or adding features.
That being said, I definitely think software engineers should be writing the unit tests and automating as much as they can - it's just that you can't automate everything.