Having been through the decision process in the past for whether to go when centralized QA, dedicated QA on teams, or automated testing as an engineering responsibility, I came away with the personal opinion that the quality of automated test frameworks has improved so drastically in the past five years or so that we really are in a different place than we were when concept of dedicated QA teams was invented long ago. Large scale software engineering is a human coordination problem (see Conway's Law and the Mythical Man Month), and the time required for engineers to write tests after already understanding the requirements is small compared to the time required for the organization to have someone else try to separately understand the same information and separately write the test. That didn't use to be the case, but today it is. I get not wanting to take time to write tests, just as I get not wanting to take time to document your code, but that's not a good enough reason for introducing the inefficiencies of having someone else try to do something that is best described as your own job (again, the economics used to be different because writing tests used to be slow and inefficient, but that is changing/has changed).

I will say however that I think you do generally still need a team (or individual at smaller shops) dedicated to tooling for automated testing to make the process of writing tests efficient for all those who are writing tests.