Prior to the distinction between UI and UX, you had (and still have) all sorts of graphic designers whose work fits into different ranges on the spectrum between function and form.

Poster designers are concerned with catching the public's eye and delivering the necessary information, but catching the public's eye is arguably more important. Other designers exclusively do branding, which is all about 'look' and hardly about 'function'.

In reply to the original point, I would say that, on one hand, how something looks is part of how it works, if you consider the entire user experience as the function of the product.

On the other hand, I think what you're saying is that you're reluctant to hire designers who only do a particular style well. I agree that a good designer should aspire to broaden their pallet, but I see no reason to condemn those who for whatever reason are not capable of or interested in that.

For comparison, consider that some fine arts produce work in the same style for their entire career (i.e. James Turrell) while others explore a broad territory (i.e. Gerhard Richter).

Branding is definitely about function, but the way branding functions is very esoteric and generally intended to be subliminal. But when you're working on branding, good designers work to a plan. They know what the client wants to say and they say it. Bad designers (like those with a style) post rationalise their work, and that's a dishonest and ineffective approach to design, in my opinion of course.

I'm not so sure. I would argue that any and all design is UI design because UX applies to everything that is designed, be it a website, a newspaper or a rocket ship.