The distinction between web sites and web applications is not granular enough to make this decision. What you should be considering as a developer/designer of a web site/app is not about what bucket Flickr or YouTube or Yelp falls into, but what specific screens should be accessible with shebangs and which screens should not.

Flickr's photo indexes and Yelp's listings and reviews should probably be accessible via regular old URLs. But Flickr's uploader screen? Adding a new listing to Yelp? If you're ok with leaving behind users who have javascript turned off, it simply _does_ _not_ matter. In those cases, why not take advantage of the snappy UX that shebanged interfaces offer?