This is a horrible idea. Punish everyone because 1 or 2 servers have issues? Mind-boggling in its short-sightedness!

Pony up & force split the server(s) causing the issue. Comp some time to the people affected by the split(s) & angry. Don't wreck things for everyone on every server. [Disclosure: I'm on Gilgamesh, so could end up one of the people 'affected & angry' - I still favor forced split over messing up everyone else!]

Heck, even if you're dead set on mandatory log outs, don't do it like this & flood the log-in server. Set a maximum x hours played before mandatory log out per character instead - maybe 8 hours. Most folks wouldn't even be affected by that on weekdays, & probably only once on weekends. Pop-up reminder at 7 hours so people could decide 'do I want to just do this now & log voluntarily, or am I in the middle of something & need to push close to the limit?'. The re-logs will be spread out throughout the day that way, but you'll still be knocking out the perma-AFKers.