To me, an aircraft has not landed until all of its wheels are on the ground.
True, but in a trike the main thing is to land gently on the mains with the nose wheel held off. That's what takes time to learn. Once the aeroplane is in that position continuing to hold off the nose wheel until the elevator runs out of authority is easy, so 'going' on a touch and go before the nosewheel has landed surely has great benefit in fitting as many 'landings' as possible into each hour, rather than the backtrack and take off that might well be required if one waits until the nose wheel has landed.
All wheels on the ground is certainly the only time I would want to be changing the flap setting from 'Landing Configuration' to 'Take Off Configuration'
On a 'wheeler' touch & go in the Chippy one has to remove one's left hand from the closed throttle, transfer it to the stick to continue to hold the tail up, transfer one's right hand from stick to flaps to raise the drag flap, RH back on the stick, LH back on throttle, open up for the 'go' of the touch and go. It takes a lot longer to describe than to do! All this time the little wheel at the back is off the ground.
Nothing wrong, in my book, with reconfiguring the aeroplane as long as it has landed, albeit with the little wheel (which ever end of the aeroplane it's on) still off the ground, though it may be a bit 'one armed paper hangar' to expect a low houred student to do it.