The web as a platform shouldn’t be constrained by two arbitrary, isolated boxes, because that’s not how it works. A software developer writing code necessarily has to get involved with stuff running on client and server devices and everything in between them out of sheer necessity, if they even want to understand how modern technology works in this space.
Now the title has been diluted to the point where it often just means “comfortable with JavaScript on both sides of the wire, plus maybe Mongo or Redis.” The original depth is gone, replaced by tooling and abstractions that compensate for the skills the term used to imply.
It’s a sad world.
-- actual (retired) full-stack engineer
Imo you can trace a lot of how devtools, particularly webdev tools, have evolved to this. They are more React-brained. Specifically they try to take state management responsibilities off their users' plates.