DBA jobs haven't been entirely offshore'd. It happens in cycles.
* Offshore to save money. Databases are a car, just follow the script / maintenance manual and everything will be okay right?
* Discover the awful quality, security, never-ending cycle of bodies, lack of retention of information, zero innovation, frustrated staff having to try to deal with them, and and most of all costs which creep up (a lot like Oracle licensing).
* Insource to qualified internal staff and retain knowledge, save money, and fix all the problems the outsourced company wouldn't.
* Now that everything is fixed, create work manuals, and offshore again. This will get out of date over time, servers will get replaced, new software comes along, and things go to pot again. Repeat.
To be fair, companies also often institute long and complex policies which stifle any kind of remediation an offshore staffer would do - because they can't. Internal employees learn the system, how to get things done, and they do it.
I work for a team that has taken over from multiple offshore companies in this way. We find all of these things and worse, really just the most awfully maintained systems around - no backups, no maintenance, no organisation, nothing. They don't even patch but they say they do! And they've paid millions (and tens of millions) for the privilege!
There's really no comparison so don't mistake the two for a second. As for automation - well - tools have made it so that one DBA can "manage" hundreds of servers at once if they're standardised in certain ways. But you'd be surprised at how many things can go wrong and how few can be automated, especially when the rest of the companies don't have proper automation infrastructure in place. Large enterprises are still fiefdoms of managers who want local employees and to retain their own jobs.
Performance tuning and improvements though are extremely time consuming. You can, for some projects, focus entirely on single digit servers for years at a time if they're important enough.