I agree that in any IT position, it is your responsibility to learn more and hone your current skill base. That's only common sense and a good way to prove to your boss that you love and respect the job.
I don't agree at all however that the life of the Production DBA is at an end. No manner of software or automation can replace the benefit of having functional understanding and experience.
For example, though planes can fly themselves doesn't mean that you don't need a seasoned pilot in a dogfight.
That kind of attitude and argument is just a lot of nouveaux CIO horse puckey. The first time the SQL instance goes south unexpectedly, you'll wish you had me sitting there watching.
Just my two cents.