Ah, but the difference is that tinkering with mixture to optimize the effect of carb heat has been demonstrated to produce quantifiable and desirable intended results toward an objective. And, any undesired affect can be instantly reversed. Not so with flap extension in some aircraft.
Nice try Step but it's not the tinkering with mixture that's the problem but the your advocacy of reducing the power after experiencing carb icing. If you are so keen on doing things by the book only, please feel free to tell us which manual you got that "trick" from?
And your point of "quantifiable and desirable intended results toward an objective" is cobblers. The OP observed that the reduction in flap had the desired result. It is truly absurd to wave that observation away with rhetoric, whilst simultaneously clinging to the belief that reducing engine power is a good antidote for carb icing!