insisting that the nose wheel must be on the ground before the "go" part is started, sometimes too late for my comfort.
A 'Touch and Go' is a way of saving time by Landing and then Taking Off without stopping the aircraft.
It is used to enable many more Take Offs and Landings to be practised in a given time and, I would suggest, that it's main benefit is actually in being able to practice
Landings.
To me, an aircraft has not landed until all of its wheels are on the ground.
Getting airborne before this happens is a 'Go Around' where the wheels touched the ground.
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'
Although a 'Touch and Go' may be the plan if, by the time the aircraft has Landed, it is not safe to proceed with the Take Off then (as foxmouth has said) DON'T
(Take Off = Always Optional whereas Landing = Always Mandatory)
If, on the Approach, the aircraft's flight path means that neither a Take Off nor a Full Stop are likely to be safe after the Landing then a Go Around should be initiated.