Most Operating Systems that have a "App Store" native application also have a Web version of their app store where applications can be added to a wish list, purchased and/or downloaded. I think it would be a good idea for Ubuntu Software Centre to also have a Web version. Since its not a good idea to download .debs, it could be done in such a way that downloads cannot be done if you are not running Ubuntu. This should not be too difficult to implement using the "apt:" link parameter. Sites such as http://getdeb.net already utilize the apt: link in a web store like service. Is this already in the works or are there plans to do it in the future? If no, why not?
I don't see anything special that will add value to current interface. USC is there to make new users comfortable. What you have just explained will complicate the matter and defeat the very purpose for USC. BTW apt: protocol have got its use especially in tutorials where user need to install packages.
If you still think the idea is still big one then propose it in ubuntu brainstorm
As James have pointed out, there is http://apps.ubuntu.com which does exactly what you asked for. You can suggest changes for UI or even changes to wording (I don't think department is the best word for example but am fine since I use only apt)