The OP is training for a CPL. If a CPL can't use their judgement as to whether it's safe to do simple checks while taxiing
Simple checks? These are run-up's where temps and pressures should be closely scrutinised and maximum rev drop between magnetos observed, suction checked at idling. If a constant speed prop, exercising of the prop is done. All the while using differential brake dragging if in a twin checking one engine at a time. What is there to gain from all this? If it is good enough (i.e. safe) for CPL holders to conduct engine run ups while taxing including twins, then it is logical to train CPL candidates to do the same while under training. Practice makes perfect. Have yet to see a flying school that teaches run ups while taxiing and certainly never on a CPL flight test with an Examiner on board.
To deliberately conduct engine run-ups while taxiing is sheer folly better known as cowboy antics, cutting corners, using the excuse to save the boss a few cents (never mind brake wear and possibility of hot brakes caused by brake dragging and costing the boss more money)