It would great to have the option when moving a website from one application server to another to leave the application on the old server for a given duration of time to allow for DNS propagation. For example, when moving a wordpress site from server A to server B, there would be an option "Delay removal of Server A application for X days". A further, and very cool option would be to perhaps lock files for writing on server A and prevent wordpress logins on server A.
I realize that this wouldn't work for ecommerce sites or high traffic blogs with lots of activity. But for small brochure sites or static sites, this would make migrations more seamless.