solve the problem permanently
Okay, here is how you solve the problem permanently, ( Yoshi P ) : Create new separate servers, like the duty servers but smaller in scope because of the intended low activity. These servers are the new place players get placed when they go into the standardized hotel rooms. Players cannot do anything in these rooms except run around. No chat or duties or anything. Only enter and exit. In these rooms they can go AFK for as long as they like and not get logged out and not take up space on the active servers. Call them AFK-servers? When the players then want to enter the active servers again they already have a spot saved for them. And all the players getting kicked out due to AFK will be placed in these AFK-servers. Players who have logged out completely have to stand in line to get on again.
Absolutely Terrible 'Fix'
Why don't they address the real problems like. You know the ones that have been mentioned constantly. People crafting and going away, people clicking a retainer or Aetheryte and going afk. Why are we going to punish people who are actively playing the game? Mid Duty? Seriously? Upgrade your auto logout and this wouldn't be necessary even slightly.
It honestly sounds like SE is intentionally making XIV inconvenient to play on large servers to try and force people to transfer servers. Oh, our bonus offers to transfers aren't making too much difference? Let's make everyone wait in hour long queues a few times a day! I can't speak for other congested servers, but you're not going to relieve Balmung's congestion without putting an RP tag on that server, or on a new NA server.