The transmission and the drive train were needed to produce a range of speeds from the narrow torque and rpm range of the IC engine. The beauty of DC motors is their ability to produce power over a wide range of rotational speeds.
Seems like the gear train might only be a source of mechanical...
I saw this design online a while back, which uses a hub motor midway between crank and rear axle. Seems like one would need a one way clutch in there someplace. Is this similar to what you are describing?
https://evnerds.com/wp-content/uploads/2017/08/cruiser-ebikes_mis.jpg
This setup is one...