If people don't like the idea of deleting unsourced articles, how about blanking them?
More precisely, if an article isn't sourced 7 days after being tagged, replace the article with a template saying "This article has been removed due to lack of sources. You can still view the article by clicking 'History'. Please feel free to recreate this article by editing the previous version and adding sources."
That way, we're still preventing the public from unknowingly reading unreliable articles (I would like to include a warning in the template, but I couldn't think of a wording that didn't apply to all Wikipedia articles - none of our articles should be relied upon for anything, really), but we aren't getting rid of anyone's work, and it's much easier to add sources to the article after the 7 days is up than it would be if you had to get it undeleted first.