Image via https://velo-gap.de/2020/05/26/duerkopp-kettenlos-1912-kardanantrieb/ who have lovingly restoreded this specimen into a rideable state
Another option for a bicycle drivetrain beyond chain, penny-farthing, the velocipede or lever-driven bicycles is just put a driveshaft on there, like a car.
There's scant information out there as to how good it is, mostly because by 1920 or so everybody stopped doing it. CeramicSpeed has some kind of vaporware around this for the roadbike I have posted about before but they made the error of trying to do this shit high-tech and with gear changes instead of figuring you could just get good at pedalling your singlespeed so it sucks.
The singlespeed driveshaft bike, all enclosed? Yeah, might be onto something
I saw a rednote post about drivetrain bikes. Based on the comments, it sounds like one of the big "bike share" companies in China used shaft-driven bikes on the first generation. Users complained about the inefficient drivetrain and said it was much harder to pedal (especially uphill) compared to chain-driven bikes
It is basically impossible to beat a chain driven bicycle as per efficiency but for some use cases and priorities a chain drive might make sense. I assume the companies here figured lower price to use would beat out efficiency, but there really is little things more aggravating then putting the power down and not getting the speed out of it one would assume