Correct, you'd need to add it to each page, but that shouldn't be a huge deal these days unless you just have tons of static html pages on your site. If your site uses some kind of templating system (Wordpress, ASP.NET Master Pages, Smarty, etc.) you should be able to dynamically add the shortened link into the document header without too much trouble.
I understand that it's not a huge deal, but that's not really the point. Do we really need to update every page on the internet with a short url? Just in case it gets linked on twitter or a shorter version is needed for some reason?
The idea isn't that every page will define its own URL. The idea is that some pages will, and things-that-shorten-URLs should then use their preference in shorter URL when linking to them. For all other pages regular URL shorteners like tinyurl and bit.ly can be used just as they are now.
Consider it in a different light -- you're running your own url shortener on the same server that the content is on. This helps to avoid "linkrot" caused by unavailable/disappearing url shorteners.
If this isn't a concern for you, don't provide this service. People will continue using other shorteners that are susceptible to these problems.
