Why?  Why shouldn't URLs persist?  Do LC shelf numbers for books change?  Does the street address of your house or business change?
 
Back in 2001 I wrote an article for Library Journal and I listed a number of reasons why digital content disappears.  Changing all your site's URLs just because you have a new director or you've chosen a new technology platform makes no sense to me.
 

Modes of digital death
The changing of the political guard is but a single cause of such disappearances. We can identify different modes of digital death: