I would argue that it's way more accurate to say this role is actually outsourced in most organizations with all the tradeoffs that come with that strategy. I begged my former employer to subscribe to a good PostgreSQL support company. Guess what the one we picked is constantly looking to hire new DBA to sustain growth...
I was in database engineering/administration position for the last 10 year on a small company. It was exhausting because management wouldn't care to rely one guy to manage the whole data stack. It was rewarding because the CEO saw me as probably smarter than I was because I knew SQL well enough to produce outstanding value as a single individual.
Often reading HackerNews I felt like an imposter because NoSQL was the new hype and database was seen as a thing of the past... well trends reverse... and people will always need reliable systems to handle business critical data.
So maybe in a few year after few major Cloud data horror story DBA will become the new trend. No one know.
But learning how to handle data? That will always be handy no matter the underlying technology.