With electric motors it optimizes differently. Torque is expensive while individual motors are cheap. Distributed propulsion makes a lot more sense.

Let's say you have one 2 MW rotor disk. Rotors are tip speed limited. Let's make it have an angular velocity a. Torque would need to be 2 MW / a.

Having four 0.5 MW disks would have same tip speed but half the span so double the angular velocity and thus each would need torque of only 0.5 MW / (2 x a). Torque dropped to one eighth, and the motor became lighter!

Now, at the one end you have a traditional helicopter with one to a few main rotors, high torque, cyclic and collective pitch in each (because torque is slow to change).

At the other end you have a huge amount of small thrusters that are directly connected to their own motor and thrust is varied by electric means.

In between you have things like intermediate number of thrusters / rotors having maybe a simple gear and/or collective pitch control.

Why is torque expensive in an electric motor? They tend to produce high amounts of torque at lower RPMs than ICEs. Even a Nissan Leaf gets 187 ft-lbs, and a Tesla motor has a flat torque curve to to 10,000 RPM.

I thought that was a generally known thing. A higher speed motor is smaller than a high torque motor for the same power. I don't think electric motors are almost ever connected to speed increase gear. It's almost always reduction or direct drive.

You can check any hobby shop or Alibaba to verify the above.

Probably related to some physics of magnetic field vs current. Would need to dig deeper into that dome day...

Well I don't really know how much torque a helicopter would need. The only number I was able to find was that a 35-foot rotor could spin about 550 RPM. Even with a smaller rotor that would spin somewhat faster, I was guessing that a reasonable gear ratio would give an electric motor plenty of torque at those speeds.

And we are back at square one where the whole point was to go multirotor to avoid the gearbox and cyclic pitch complexity.

In a car, it's a bit similar thing. With a combustion engine it optimizes to a single engine with fixed + variable ratio and shafts to the wheels and things like differentials. Lots of places to have oil, to maintain, to break, being heavy too. Tesla has 1-2 electric motors with a fixed gear ratio of about 10. Some concept vehicles have a direct drive motor near each wheel or even inside the wheel.

The electric motor has different characteristics than a turbine or a piston engine. Hence it can affect the whole machine design.

Exactly right. Aviators know that a propeller blade provides thrust/lift but also induces drag. Given a certain power output, the more blades you have, the more drag you have, but you don't get any more lift/thrust. Therefore, if efficiency is what you want you really want as few blades as you can get away with. Normally more blades are a consequence of other design constraints, such as how wide you can realistically build a propeller blade before the stress causes it to disintegrate.

Small multi-rotors have to spin faster to compensate for their reduced efficiency, leading to the characteristic drone sound.

Computer cooling guys know this too... bigger slower fans move more air and do it with less noise.