No it's not their job, and I'll try to explain why I think that.
Apart from the remit being just too broad, designers in any case are
part of a complex team that deal with a multitude of functional,
non-functional, regulatory and financial requirements.
Now, we have many different definitions of "designer", which I am very
aware of, but I believe that, in some circles "designer" has become
romanticised and extended to include a set of perceived "magical"
powers to "deliver what a boss wants". That is a distortion of the
role to something grotesque.
Speaking from a domain in which I have expertise; in sound design a
great battle ensued between designers, users (audiences) and the
'bosses' (studios and publishers) as to how music and films should
sound. You probably know this as the "Loudness Wars". I think it
remains a textbook example of misalignment between technical, artistic
and financial factors. It also remains an example of why I think
"Markets are a myth" [2].
Despite listeners saying over and over that they "Don't want it", the
producers, through a mess of internal motives (mainly financial),
repeatedly foisted their values onto them, being obsessed with what
they think users want in preference to flat-out contradiction that
would be evident in even the most cursory market research.
The job of a designer is to balance factors, and in a sense act as an
advocate (stand-in) for the user by mentalising their actual
needs. It's a very demanding and complex skill. Doing "what your boss
says" is absolutely not it and reduces a designer to a tool.
On the other hand, a job of the designer is also to listen to expert
technical advice outside of their skill-set, and so must not get
carried away with any grand "aesthetic vision", wanting to be Steve
Jobs.
A hard line to tread, and one requiring strong will and ethics as well
as judgement.
[1] https://en.wikipedia.org/wiki/Loudness_war
[2] https://news.ycombinator.com/context?id=32463541