Do external motors really produce more torque using less electricity? If so, how? If the issue is sub-optimal RPM in hub motors, then why would moving the motor outside the hub help with that? I am looking for some no-nonsense technical explanation of the pros and cons of each design.
Humans are peculiar. Humans produce power best at less than 100 RPM. Very similar to steam engines and very dissimilar to internal combustion engines, turbines or electric motors. Bicycle wheels rotate at 250 RPM when riding on a flat road. Thus, you need about 3.2x gearing if riding on a flat road.
250 RPM for electric motors is extremely low. Typically, optimal motors like to run at 10 000 - 20 000 RPM.
There are ways to make motors generate useful power at 250 RPM, but these make the motor heavy, expensive and perhaps inefficient.
Not only that, but a hub motor requires a reaction arm and electric cable to the hub, making changing a flat tire needlessly difficult.
The best e-bike motors are at the bottom bracket and use reduction gearing. With reduction gearing, you can reduce speed by more than 10x and improve torque by more than 10x. It won't let you use a 20 000 RPM motor, because such a motor would require 200x torque multiplication and 200x speed division. But, by creating a slower electric motor AND by using reduction gearing, it is feasible to build an e-bike that produces useful torque.
If seeing a hub motor torque somewhere, don't believe it! It is probably the torque when the wheel is not rotating. With increasing speed, the torque reduces.
Furthermore, the bottom bracket motor torque is affected by the drivetrain gearing too, so it is possible to produce both high speed (high gear) and high torque (low gear) using the same motor.