I agree that a beloved small biz web site can have the "voice" and texture of a Mom-n-Pop outfit - BUT it must have the functionality that will help people solve their problem. Otherwise people are way too busy to use your site, and they won't if it does not effectively help them.
The internet is rather disembodied, and I always love it when a site features pictures and bios about who is actually "there". If it's Mom and Pop, then put it out there and embrace it. Just be accountable and help your customers get what they need, and quickly!
I always choose small businesses to deal with whenever I can. I'd rather not become embroiled with employee #502 in department X, since they are probably suffering cubicle stress! I'd rather have the business owner come in from the garden and check emails with dirt under their fingernails, they can give me more personalized attention!