What I consider the best instructor I ever had (though he was a cowboy in every other way, and eventually vanished to get away from a number of people who were looking for him) taught me the single most important thing I ever learnt (for the sort of flying I do which is non-aerobatic and flying mostly from A to B, with some cloud hole drilling thrown in) which was that one should always TRIM
for the desired airspeed in all phases of flight.
Yes of course it is true that not using the trim wheel and just pushing or pulling the elevator back and forth will most definitely change your airspeed
because that is what the elevator trim wheel ultimately does anyway, but if you don't TRIM
you are flying an aircraft which wants
to fly at an airspeed that is different
to your present airspeed, and this is going to bite you when one day you get distracted and lose concentration and don't watch the ASI and you happen to be trimmed for some low speed and you have also reduced the engine power for some reason.....
If one is going to teach somebody to fly "instinctively" then there are empteen ways to achieve that, and provided he is on the ball at all times none of these should kill him. But, and with the disclaimer that I have only 12 years and 1500hrs, all that I have seen over that time supports my view that the safest way to fly is to fly by numbers
i.e. know what power settings should give you what speeds, and trim
to achieve those speeds. If you don't do that, flying a plane is a lot more work and you are constantly chasing the thing.
Take that solo student who got killed when Southend ATC asked him to do an orbit. I don't really think his instructor ever taught him to fly to his plane's performance numbers. He was probably like me - in all of my PPL training nobody ever explained to me what the trim wheel does. I was told that it is used to reduce the pressure on the elevator, so your arms don't get sore. Well, that's true, but that is not the primary function.
Not all instructors are good - by a long way. The first one I had had 150hrs TT at the time (or so he told me).