For both commerical gaming servies and the odd LAN party, a mechanism to transfer a game from a (possibly dedicated) server on one machine to a (possibly dedicated) server on another machine might be convenient.
Flexibility, graceful handling of hardware maintenance situations. Some have suggested that ID tends to neglect LAN play a bit (try changing a map manually, you don't get to see scores, but are just slammed out in the console) because Americans with their low phone charges tends to play on the Internet. One annoyance I've often butted heads with is when the server has to quit, (for various reasons, player has to leave, machine needed etc) the game just ends(and you still don't get the see the scores!).
Security. Gameplay will still stutter during passover. A lot of configuration and implementation overhead for what is effectively a minor nuisance and no priority whatsoever with lack of persistence and multi-server/RPG elements in Q2/Q3.
Strategy games ("Red Alert","Age of Empires", "Total Annihilation" etc) implement mechanins in which a server transfers the current state to another player before shutting down. Another player gets the message that the server has quit and he is now the new server.
A full pass-over would be a generalization of transmission of player data from server to server (multi-server support), and of a reworked savegame format (suitable for wire transmission). It also could employ autodownload mechanism for server-server transmission of map data and resources.