There are storage administrator jobs. Years ago I was a Storage Sysadmin that managed PB's of storage on NetApp and various EMC related products (clariion, vmax, datadomain). I also worked with backups, and managed the Unix servers (fun /s). Since then I've moved to a Cloud Engineering focused role.
My path was Helpdesk -> SysAdmin -> Cloud Engineering
I will tell you that being a storage admin is a very specialized role and IMO it's slowly dying out. The only place you'll find that role is large companies that have on-prem (data center) metal. I decided to move more to the engineering side because I didn't think the storage admin path would play out well in 5-10 years time. From what I've seen of my former co-workers that were on the team, about half have moved on to large companies to manage storage, the others went to more cloud related jobs.
Most storage is so easily managed in the various cloud offering that there's almost no point in paying a person to solely manage it.
I'm more than happy to expand on anything if you'd like. You can DM me if you want more specific info. I don't like to be too specific on public forums.