Electrical Conducter Size

You've very aptly listed here many of the desires or advantages of using small gauge wires in a motor. However, I believe the OP wishes to know why wires in a motor can be considerably smaller conductor diameter than the wires feeding the motor.

First there is a common layman's misconception about the current capacity of a conductor. The maximum amount of current that can flow through a conductor is not limited by the conductor. The best example any technician can see that proves this is an examination of any glass ampule fuse like a 3AG style fuse. The fuse element inside is considerably smaller diameter conductor than the wires to and from the fuse. Yet this thin conductor must handle the same current as those wires because it is in series with those conductors.

Assuming that the voltage remains constant, the maximum amount of current in a circuit is limited by the impedance of the circuit. The series component with the largest impedance will dominate what will be the maximum current in a circuit. Now the problem with pushing too much current through a conductor is the self heating of that conductor may overheat the insulation to the point of ignition or even liquefy the wire of that conductor. The tiny conductor in a fuse deliberately has no flammable insulation and the glass envelope and atmosphere inside is designed to contain the arc flash of the circuit opening.

So the wires in the motor are at the location that sets the current. The very thin insulating coating of magnet wire maximizes the number of conductors that can fit in a space. This insulation usually has a high temperature tolerance. These wires are fixed in place so a solid conductor can be used. Magnet wire in a motor is also in contact with core material. Thermally this core material will act as a heat sink. The mechanical motion of the motor will also often simultaneously draw a coolant through the motor.

In contrast the wires that feed the motor will not be in contact with a heat sink. They will also have to flex from motor vibration if not actual movement. Frequently feed wiring will feed additional circuitry (starter circuit, status indication) that can significantly increase the current loading of this wire.