Carb heat should be (in my opinion of course) set into the cold position when you are able to glide to the runway in present configuration. This is usually at least 50', more likely 100' from the runway, so I think the workload isn't as high so the average student would get overloaded. Besides, on Cessnas where you actually need carb heat for every approach, carb heat lever is conveniently put right next to the throttle so it shouldn't be too hard to press the carb heat "button" fully in when reducing throttle to idle. On Pipers that's another story with lever placed far away, but it isn't required for normal approach.
I think that setting carb heat to cold on the ground during touch and goes isn't as damaging to the engine (I wouldn't want anything but clean, filtered air until venturi in the intake system) as is to the performance on climbout if left in hot position (mistakes happen, as we are all just human). For example, doing touch and go on short (yet long enough) runway with obstacles at the far end, I would always prefer to select carb heat to cold on short final then on the ground.
Oops, haven't noticed until now that you operate PA28s. Why do you even use carb heat during normal (powered) approaches, since Piper's (at least 28 and 38) intake system passes the oil sump on its way and is therefore naturally heated in the process?