This is not initial training on fixed gear trainers.
No, it's multi engine training in light piston twins.
It is also good practice not to touch anything besides throttle and foot brakes when on the runway, I retract flaps only after clearing the runway.
Hopefully your students will never need to go around once the wheels are on the ground. If they do, they'll do it without the benefit of having proper instruction. If you can live without giving proper instruction and covering all contingencies, so be it. It's your conscience, your ticket.
Of course, it's the students life, and that of their passengers. Personally, I'm not comfortable releasing a student who isn't fully trained to proficiency. That includes light, piston twins.
One solution to introducing a rolling go-around is to have the instructor handle the flaps and reset cowl flaps as the student flies. Introduce additional workload progressively, and perform drills on the ramp in a quiet, dark airplane; no power, just an instructor and student doing blindfold drills to find the proper controls and identify them. Simple. Safe.