My philosophy regarding engine failures/loss of power, total or partial, is that there are 4 potential causes: mechanical, fuel, ignition, icing. If a pilot mis-selection, inadvertent or otherwise, has been made then it typically falls under fuel or ignition. If this philosophy is taught clearly then it applies to all piston engine aircraft and only the detail of how to analyse and potentially correct the cause needs to be taught for the type being flown.
The other generic aspect to consider is with a variable pitch propeller: leave it as set/fine if a restart is to be attempted, select coarse if the engine is to remain shut down.
I am not involved in PPL level instruction so I would be interested to know if these philosophies are taught at this level and if it is considered reasonable for an ab initio student to have the capacity to to think them through.