Certainly only licensed or government aerodromes may be used for ab-initio PPL SEP training. But regarding a flight with a student to an unlicensed aerodrome for maintenance purposes, things are less clear.
I'm not sure they are. Articles 101 and 130 make no provision for a flight to be broken down piecemeal into instructional parts and non-instructional parts. If the flight is for the purpose of instruction in flying then it is for the purpose of instruction in flying. You wouldn't expect a public transport flight operator to be able to say "it's OK to land at this unlicensed airfield because I only charged the passengers for the first 55 minutes -- the last 5 minutes before landing were free"
If, for example a flight from a licensed aerodrome culminated in a landing at an unlicensed aerodrome, I would consider that the student shall not be allowed to control the ac for flight within the unlicensed aerodrome circuit, including the landing. So the RF must not allow the student to log the entire flight, nor charge him/her for the entire flight.
If that means, "must not allow the student to log any of the flight, nor charge him/her for any of the flight", then we agree.