Has anyone successfully proposed a website replacement to a small business?

Say there is a small business in your city that should be competitive as it has very low product prices and good service, but doesn't get enough exposure and has an perhaps undeservedly poor reputation due to an awful website that has severe usability problems, very poor quality copy, and does silly things like putting most content in PDF files linked from various places on the site.

Has anyone successfully initiated a proposal to rewrite and maintain a website for a small business, or is it a case of "things don't work that way"? The proposal might include a discussion of the problems with the current website, the consequences of these problems in exposure and revenue, and an overview of the solution that would be offered.