Back when I started 17 years ago that’s how it was. We were just Designers. It was later on when agencies started charging clients for each step of the design process that this fragmentation came to be. First you charge for research, then for wireframes, then for “Look & Feel” and so on. Subsequently, each step required a dedicated person/team to it.
I completely agree that a designer is naturally a generalist. And as I like to quote Heinlein “…specialization is for insects”.