The power supply can easily overcome the difference in resistance but it does have to generate additional power to do so. Assume the winding current is 2A (amps) so the formula for power is I^2 * R
Rough Power Estimate Total Circuit
22 AWG = 6.23296W
18 AWG = 5.60864W
Power Excluding the Motor - Cable only
22 AWG = 1.03296W
18AWG = 0.40864W
So about 0.6W more is wasted in each 22 AWG wire compared to the 18 AWG wire. That’s per circuit so 4 Motors x 2 Windings = 8 circuits so about 4.8W of wasted power and more work the 30W power supply has to do. So is 18 AWG better technically — Yes; but 22 AWG does work and works across many machines so it’s an efficiency vs cost tradeoff design decision and I can’t fault the designer for it given the target cost of the machine. I’d say the designer was successful given there are not machines failing all over the place.
Again, I really need to finish my coffee as I’d bet there is an error somewhere in this musing. This brings back memories; I did the motor driver designs used in millions of IBM typewriters and Laser Printers during my career.
OK so the point I was trying to make was that the recommendation seems to read “if you need to replace the wires for your motors and limit switches, you should get shielded wire when none comes with the machine of a larger gauge than what the machine comes with”. That appears to say that the wiring that comes with the machine is inadequate, if you replace the electrical wires, get thicker wires that are shielded. While it may offer better performance, I don’t know that you really want to say that without better qualification.