That is true, although direct drive without a tranmission simplifies a design and reduces driveline losses. IT all depends on the application. IIRC Tesla originally had a two-speed gearbox in the Roadster but dropped it because of reliability, and went to increasing the engine RPM instead.

You're assuming that torque remains constant at higher angular velocities, which is not true in most electric motor-drives.

It doesn't stay constant. I didn't assume it stays constant either.

Your maximum torque can be extracted by the right gear from the maximum _power_ peak. That means even with diminishing torque with angular velocity, if it diminishes only slowly, it's still worth going to higher angular velocities.

Example: Say if you have a motor that has 100 Nm of torque at 100 radians/s, which is 10 kW of power, and 80 Nm of torque at 200 radians/s, which is 16 kW of power.

And further, you specify that you need to have the maximum torque in the wheels at 10 radians/s.

With a 10:1 gear ratio, when your wheels run at 10 radians/s, your engine runs at 100 radians/s and provides 10 kW. Thus the torque at the wheels is 10000W / 10 radians/s = 1000 Nm.

With a 20:1 your engine runs at 200 radians/s and 16 kW and wheel torque is: 16000 W / 10 radians/s = 1800 Nm.

More torque at the wheels with less torque at the engine!

Of course, with a fixed ratio, the latter vehicle would be limited to a lower top speed. That's why we have gearboxes and variators etc.

With an electric motor though that has better torque at lower speed, you can often try to design for a compromise so that you don't need a gearbox and might not even need a gear ratio at all.

I used SI units since you get extraneous confusing factors otherwise.

Here's an example of a brushless motor power vs rpm. You can get maximum torque for your selected angular velocity by operating at the max motor power and using the right gearing. http://www.mcpappyracing.com/images/dyno/chart_power.jpg