I don't think it's totally unreasonable to expect a web designer to find a way to show their work off online. Note, however, that in doing so you might end up

I don't think it's totally unreasonable to expect a web designer to find a way to show their work off online. Note, however, that in doing so you might end up overlooking some really great designers who don't have the time or expertise to show everything they've done online. Depending on your needs, it might end up being better to go with a designer who has a lot of experience working on non webby things (i.e. print). Not that there aren't a lot of amazing web designers, but I've noticed that there tends to be a lot of groupthink in web design. Certain things become trendy, and many web designers end up just following these trends. Perhaps one of these less web savvy desginers have a more diverse background that would help you come up with something that really stands out.