Is it even possible nowadays to be a generalist? In science something similar happened. There was a time where some people knew pretty much in every science field, chemistry, physics, biology etc. but the amount of knowledge grew and it become impossible to know enough in every field. Maybe game development isn't any different. You either become an expert in on field or your knowledge is to superficial to actually he…
The main issue is mindset, a programmer might cut short a design to save himself time, an artist might simplify the gameplay to not put in as much effort, and a musician or writer might not focus as much on the visuals because they get caught up in how it should it sound/read etc. But they certainly can take on other roles. If you have any experience with start-ups and indies or freelancing you might find yourself take over roles you didn't expect originally. On smaller teams this goes a lot further.