Many of those re-wound motors are also completely misunderstanding the point. Electric motors are inefficient at producing high torque at low speed – they’re efficient at producing high power at high speed. If you wanted to get more torque/acceleration/power at low speeds, you should use a reduction gear and sacrifice your top speed, because then your batteries would last about 30% longer than by simply re-winding the stator for higher magnetic flux.
Also, rewinding the stator with more turns per coil increases the inductance of the stator, so your top speed drops anyways; impedance is frequency dependent, so as the drive frequency increases the motor starts to draw less current and puts out less power. You essentially shift the peak power to a lower RPM.
So while you gain torque and power output at low speeds, you lose power/torque at high speeds. You could do the same simply by changing the final gear ratio of the bike without adding the extra weight of all that copper wire, which would let the motor run faster and more efficiently as it is.
The problem is that VFD is not efficient below 40% of the nominal design speed of the motor, so re-winding the motor for a lower speed range is not as efficient as simply gearing it to run faster.
It’s not very different for PMDCs. The main point is that below some frequency the impedance of the motor is not sufficient to keep the stator current from saturating – typically by hitting the output current limits of the controller – and once that happens you start to waste power.
As long as the current keeps growing, energy is being stored in the magnetic field, and that energy gets transmitted to the rotor. When the current stops growing – when it hits coil resistance or controller limits – then you’re simply heating the copper without adding any energy to the field, and the longer you keep doing that during the cycle the lower your efficiency is going to be. At the ultimate low frequency, trying to maintain static torque is going to have zero efficiency because the rotor does not turn, therefore it’s not doing any work and there’s power input but no power output.
As a rule of thumb, VFDs become useless below about 25% of a motor’s design speed, and if you need to run the motor that slow, you should either double the number of poles or add a reduction gear. That however doesn’t mean that people won’t try, and most commercial electric cars for example basically sacrifice efficiency for not having to include a simple two-speed gearbox.