There's a third factor. Ev's need to support fast charging. So they need to do support super high voltages and currents. That's much of the expense of a powerful EV. A powerful motor is relatively inexpensive in comparison.
If you can charge a car in 20 minutes, the battery and some other circuitry can support discharging in 20 minutes, which is an insane power level.
That's not exactly true. There is some shared wiring between the DC fast charger and the motors, but not so much that the powerful motors are "free". The wires that run between the motors and the battery are long.
I think the larger third factor is regenerative braking. That uses the exact same circuitry as powering the motors, and if you want to be able to brake quickly without the brake pads, that's a lot of kW to be absorbed.
Any way you cut it, I agree, it's an insane power level.
A powerful motor needs more copper between the battery and motor and more silicon in the inverter to handle the current. The motor is also heavier. This is all extra cost.
All that fast DC charging requires are cells capable of handling the current.
You don't get a powerful motor for free just because you can fast charge.
If you can charge a car in 20 minutes, the battery and some other circuitry can support discharging in 20 minutes, which is an insane power level.