Switching my title from "System Administrator" to "SRE" within my last company resulted in a job family change and a 10% raise (I had to show I could code as well as a software engineer in order to make the switch).
When I left that role, having "SRE" on my resume instead of "sysadmin" was (probably, I don't have any strong evidence for this) instrumental in getting responses when I applied to "Software Engineer" roles at selective companies.
I think there is a bias against roles that don't code, and especially roles that sound outdated.
A lot of larger companies and managers in those companies don't understand what DevOps is, what SRE means or anything like that. They just know Ops and Dev, and your previous job title is probably the strongest hint they have to work off when they categorize you. Getting lumped in with Ops is (probably) a big hit to your earnings potential and limits your future options if/when you decide to move.