Sure, but do you think the formal automated testing could be integration tests and avoid unit tests altogether? Esp for microservices I think this could be the best way to go. So much simpler and confirms you're getting whats in the spec.
I think that "good coverage" with integration tests certainly is possible. But to get that coverage /confidence you typically will have to make other test enabling code that while not being DI and stuff that affects the production code still is code. I was at a place where it was practical to drive most of the testing this way and we had to produce fragile and complicated code to set up the database in the proper way. And of course the tests were too slow so we made lots of effort to optimize. And in the end the coverage was too low but we had enough confidence to release often. That confidence was partly due to our customers being so deep in our product without a proper competitor so the bugs the customer found was not a big deal! :)
Integration tests can become heavy for complex systems, and unit testing then gives you faster test-modify loop when developing code.
I think they could be any kind of test that makes sense, so yes. I think the important bit is the automated part.