ok in a brushless, ignore firctional losses, 7-14v = 2x RPM original 24T to 12T=1x RPM and by RPM I mean at THE WHEELS.
In theory, at full throttle the motor will run 1x speed at 1 volt and 2x speed at 2 volts at the motor shaft, gearing dont matter.

Another thing we need to consider is Drag I was not including drag, and I mean drag caused by weight.
Example, you ever hear of lighter crank shaft pulleys? They DO NOT increase horsepower, they decrease the time it takes to go up into the rpm curve through decreasing drag. When you increase your pinion size, you increase drag when you accelerate. Once you reach top speed, it dont matter.

So.. ignore drag and friction. double the voltage of the motor and half the gear ratio you will get the same RPMs but you will get more power because you will have more torque.

And like you said, P=I^2R or V^2R (2V)^2=4V so you'll have 4 times power to agree with the law.

My point is this, just try to imagine the motor fighting the drag during acceleration, we both agree this causes higher current draw.
Yes, if you decrease the pinion size in this situation the current draw will be less because it will reach top speed quicker.

When I said no matter the gearing, i meant at constant rpm or desired speed (cruise), the gearing doesn't affect the current draw.
Also, frictional losses remain relatively constant in the bearings, gears, etc.