I hate to rain on the parade, but many of the ancient Japanese inn entries are a bit dubious. They're mostly based on traveler's reports that there was an inn

I hate to rain on the parade, but many of the ancient Japanese inn entries are a bit dubious. They're mostly based on traveler's reports that there was an inn at X/a new hot spring was found at X in year Y being conflated with the fact that there's an inn at X now: they may well be the same, but it's hardly ironclad proof of continuous operation.