For those of us that like long slow-paced sessions, being able to change the difficulty "on the fly" would be a very nice to have feature.
By long, slow-paced, sessions -- I'm talking about games that might take 40-60 hours of play to finish, spread over a few weeks. I might start at "challenging" but start to pull way ahead of the AI. Rather then toss 10-20 hours of gameplay, or just gifting them techs / planets / etc. willy-nilly only to have them fritter them away again, it would be nice if I could bump the difficulty to the next level and see how the AI does from that point forward.
Look at it as a way of salvaging a game session that you've already played for 10-20 hours, so that you can get another 20-30 hours out of that map before it is over.
There could even be a game option where the AI difficult starts at your "preferred" level, but can automatically change based on how far ahead / behind you are compared to the rest of the AI players. You could allow it to only increase the difficulty, only decrease it, or change it either way (and set how aggressive the dynamic difficulty scaling is).
So if you're getting crushed, the AI starts being more likely to make mistakes that you can capitalize on (easier difficulty). While if you are starting to run away with the win, the AI could be instructed to step up a level (or three) in difficulty, spend more CPU cycles and use smarter algorithms to try and stop you.