Who knew that a C172 or PA28 could be so complicated?
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.
Better read your C172 POH again mate! Nowhere does it say T's & P's should be checked (let alone "closely scrutinised") during a run-up. I would suggest to you that "suction checked at idling" be done when the engine is actually idling and not during a run-up.
I'm not that special, but I could do all that by glancing inside at the appropriate time while keeping an eye out where I was going.
All the while using differential brake dragging if in a twin checking one engine at a time.
Please don't put words in my mouth. Show me where I suggested doing this in a twin or a constant speed prop.
Have yet to see a flying school that teaches run ups while taxiing
So what? Like I said earlier, I was relating my experience. Yours is (obviously) different.
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)
ROFL! The horror! Where's Helen Lovejoy when you need her?
As for brake wear and "hot brakes", sure if you spend 1-2 minutes doing a run-up but who does that? Like I (and plenty of others) have said, run-ups in something like a 172 should only take around 15 or so seconds. If the aircraft is flown every day, and operated correctly (i.e. as a typical charter aircraft would be) this is all it should take.
As I said earlier, a CPL is going to be required to use their judgement. If they judge that the circumstances and their competence can allow them to do run-ups while taxiing, I can't see a problem.
I'm happy to pay for the small extra cost of doing an engine run-up, prior to every take off.
Not everyone shares that opinion, particularly as it's not a requirement.
DIVOSH!