strangely, usually on the left not the right
It's a military thing.......when one progresses to something a lot faster the throttle by convention is on the left/ stick in right hand.
Many military piston trainers are modified so that the pilot in command (student when dual) sits on the right thus using left hand for engine controls. The instructor sitting on the left uses the extra throttle provided to their left.
Those that are not so modified, the pilot in the left seat still has a throttle on their left.
You need to look at the certification standards with regard to positioning of instruments.
Guidance is not LAW,
Quite right but it is a brave person (some would say insane!) who can stand up in court after an accident and say with confidence that they know better than the CAA despite having had an accident as a result of not following CAA guidance.
Insurance companies might think that they pose an unacceptable risk.
Regards,
DFC