Looking some more into Narita Airport and stopovers, there appears to be a "International Passenger Service Facilities Charge" in Japan of ¥2040 (~$20)
The details: Applies to International Departures from Narita.
Exemptions: Infants and International transfer pax connecting within same calendar day.
So I don't believe that this would apply regardless of whether the person enters the country or not - as long as they aren't there overnight.
Doesn't appear to be any other customs based/immigration type taxes that would apply.
I don't believe the airport would be concerned about the connecting bags lying around 'out back' while the pax are away from the airport - or at least I have never been made aware of this being an issue or heard anything different.
Whenever I have more than 3-4 hours spare at an airport, then I'll leave where possible and visit the town for a stroll, bite to eat and relax away from the airport. Never had any dramas (but always very cautious of my time and ensuring that I am back at the airport in reasonable time for my flight).
Note though, that is part of the Qantas (and some other airlines) conditions of carriage that they expressly prohibit you from leaving a transfer airport. I presume this is to ensure that they aren't hit with fines for immigration offences (eg no visa) and to ensure that any liability for anything that goes wrong is on the pax. Under Qantas rules, this could lead to denied boarding.
Flying with Us - Before You Travel - Conditions of Carriage - Long
0.1 Refusal of Carriage
Even if you have a ticket and a confirmed reservation, we may refuse to carry you and your baggage if any of the following circumstances have occurred or we reasonably believe will occur:
<snip>
* if you ask the relevant government authorities for permission to enter a country in which you have landed as a transit passenger