I was going to reply to this as well, and add that this is the only game i've played that doesn't have a timer. GW2, STO, SWTOR, ESO and I'm sure someone told me WoW has as well.
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WoW definitely kicks you out for AFK.
Another thing to think about is that current active log-ins partly(?) determine whether you can create characters on a server.
Sadly, an AFK timer wouldn't even help a server like Balmung because the RMT hammer the server for new characters 24/7 (you can see 200+ garbage-named lv1 THMs and ARCs logged in moments after every maintenance)
I can't see a reason to kick out afk players. The game is looking empty enough already. Keep the mannequins in the windows. It doesn't impact server performance.
They should just make them perform progressively more embarrassing/absurd emotes as time goes by. It would be funny to come back from afk to see your character surrounded by a wall of beer cans, duct-taped to a pole, or digging a hole to nowhere.
When Stormblood comes out, SE will bring back the 'afk-kick' thing again, as well as the multi-server zone or whatever it was called to make the release of the expansion smooth. Possibly smoother than HW's.