I think it takes a lot of effort (and money) to build a webshop though. It's not just about putting up an e-store. You have to take photos, provide product descriptions, sometimes measurements, give customer service, do shipping, etc.
Some stores I've talked to say they only do 10-20% of their business online, which makes the expense barely worthwhile. Obviously, the hope is that the web portion grows, since you can ostensibly serve a wider audience, but that takes a lot of resources. I think it's a different business (one that doesn't necessarily have to complement your local business if your local customer isn't really the same as your target global customer).
AFAIK, the "phone in only" things are usually a request on the part of the designer, sometimes as an effort to favor certain stores over others.