This doesn't address the question "why a chain" though.

Many motorcycles have grunty torque, gearboxes, and no chain: https://en.wikipedia.org/wiki/Category:Shaft_drive_motorcycl...

The BMW R 100GS Paris Dakar was the bee's knees for crossing the Tanimi Desert: https://www.motorcyclespecs.co.za/model/bmw/bmw-r100gs-pd-89...

Shaft drive is more expensive to produce, tends to be a little heavier, and usually has more friction loss.

Shaft drive delivers power better, wears less than a chain, easier to maintain.

Swings, roundabouts, and tangential from answering why "Torque, electric motors need gearboxes" doesn't answer the progenitor question "why chain".

My bike vendor likes chains. They wear more easily, but are easy enough to maintain and change. Basically everything old school bike like has maintenance/repair advantages.

I'm not sure I agree, but more when compared with belt drive and internally geared hub. But then again, I believe him that those are hard to repair when they fail (even if they are sturdy until then).

I also prefer shaft drive over a chain. Much less hassle and if not punished, can be almost maintenance free. A chain is easily worn and can even rust away just sitting there.

[delayed]

Yes, the gear reduction is done in the "gearbox" in those. Some bikes use chains to do the same.

If you have elecreic hub motors there is no room for these between the hub motor and wheel.

So, we appear to agree, there could be a shaft or a chain between the gearbox and the wheel.

Ergo, the existence of an off hub gearbox neither forces nor requires a chain to be used to transfer power.

The arguments for why use a chain Vs why use a shaft are not predicated on the existence of a gearbox.

Shaft drives are less efficient than (clean) chain drives. Chains are just really, really good (outside of extremely dirty conditions).

Chains wear down, as do gear wheels.

They both have their pro's and cons, I've a few hundred thousand km's across the globe each with both shaft's and chain's.

Thank you for expressing your personal opinion though.

Everything wears down.

Chains are objectively more efficient than shaft drives -- it's not my personal opinion.

The two major downsides for chains are maintenance and longevity.

The main benefits to shaft drive are longevity and ease of maintenance.

That's objectively more efficient to those that travel a lot in harsh conditions.

Opinions are almost always personal.