Just completed a trip to Seattle in J that included a daytime layover of ~13 hours at ICN. Was shuttled to a hotel in the airport town. The name of the hotel is the Hotel June and it's a bit of a dump.

Also the airport town is the pits. We felt like we were imprisoned and after a few hours of napping we elected to return to the airport and take a bus into Seoul for a bit instead of waiting it out at the hotel.

I do think it's nice that they offer the service but frankly I seriously doubt I'd take them up on it again. The in-airport transit hotel is a far better option even if I had to pay for it myself. For an overnight stay I'd go into Seoul.