You can have generalist characters in class-based systems: 1e's Cleric/Fighter/MU.
You can have archetype characters in skill-based systems.
My experience is that, in general, even in purely skill-based games, you'll have more fun if you specialize.
In the long run, many skill-based games--unfortunately--encourage generalism. Plus, you can have "broken" mechanics like the Gurps "put a high score in DX or IQ & be good at everything physical/mental." (Just an example...I wouldn't want to get into a discussion about that again.) & occasionally the jack-of-all-trades character is fun. But, in general, playing to type ends up being more fun.
I've come to see classes & skills as two extremes of the same continuum. Classes are nothing more than really broad skills. I could say that Bob has training in sword-fighting, hand-to-hand combat, riding, jousting, courtesy, &c. Or I can just say that he's been trained as a knight. Each has advantages & disadvantages.
In any case, are archetypes still useful? Of course. Do game mechanics need to be built around them? Mostly no.
My caveats are that a skill-based system needs to consider two things:
- Do you reward specialization or generalism?
- Are different types of characters modelled at the same level of granularity? Do you need 20 skills to build a knight but only 5 to build a mage--or the other way around?