The name came along for the petrol assist motors on bikes just at the moment sales were stopping in favour of the increasing scooter sales. In fact both products overlapped, contrary to popular belief the scooters took years to really take off. There were still some autocycles around from Excelsior and the like, those being pedal and petrol 98c jobs, and I think they probably helped with the gradual name transfer, it appearing quite a lot later in place of scooter.I never did understand how low powered motorcycles and scooters without pedals came to be known as mopeds. By definition moped means motor assisted pedal cycle. As you say, the perfect description for our machines.
With these multiple products around, I think public confusion probably played in big part in the misnaming. The OED doesn't help by getting things wrong as usual, thinking a moped is a low powered motor cycle.
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