[glassdoctor]

Let's not forget that a motor is designed for a certain range of voltage and won't work well if at all, if you go too extreme.

Please consider this, back to r/c stuff. I think this may clear things up:

Take a normal r/c car 540 brushed motor made for running on 6 cells and try running it with 3 cells, or 12 cells. What happens?

It will barely move a car on 3 cells, and it not draw twice the amps or produce equal speeds as it did on 6 cells. Under your arguments, we should be able to just gear up and have equal performance at double the amp draw, since the motor is a constant source of power under changing voltage.

It would be ballistic fast on 12 cells for a short time until it blows up, and will produce much more power, indicating much higher amp draw. No matter what you do with gearing, the increase in power will be dramatic.

Notice it doesn't magicly become a self-current-limiting device on 12 cells and only produce the exact same amount of power as it did on 6 cells, while drawing only half the amps and thus doubling runtime. Again, even changing the gearing will not make up the differences.