A good designer will have the visual sense that can be applied to almost any medium. A really good designer will know the full potential of that medium.
Right here I am referring to website design as this is very much our speciality. Quite commonly we are asked to work with other designers, often the ones that developed our client's branding. So on the face of it the best people to be involved in the design of the new website.
To ask a designer to understand the potential of what a good responsive website can do is expecting them to acquire experience in some very technical aspects of how we put together a website. Assuming they don't have this experience, some do, it is up to us to communicate fully with the designer at the outset of the project. It is up to the designer to understand what is on offer and work with us to produce a magical result for our clients.
So if you are looking to hire a designer to do your website design separately from the web company who will be developing it make sure they are working together at the outset. Otherwise the result could be, at worst, a design that is unworkable for a live, dynamic site and at best missing out on much of the new site's potential.
Don't put yourself in the position where your designer presents the finished design to the developer only to be told it won't work. It really is better if we all work together from the start.
Cavespider, putting the team into work