A gearbox is just dead weight for an electric vehicle. Especially on a bike.
The battery depletes its charge according to the used energy. A gearbox does not change it , it adds energy loss in the system.
Look at the Porsche Taycan. It has a 2 step gearbox. And it looses against the tesla Plaid in every way.
In theory it can be proved without a doubt the gears would have a lot of disadvantages. But consider a real world application of a single speed bicycle and a 21 speed bicycle, why does the 21 speed bicycle climb up hills better have a higher top speed and the rider has less fatigue than if the same rider was riding a single speed bicycle.
With 21 gears we are adding more weight, more friction, more maintenance, more expense and more moving parts so in theory it should be a disaster but in reality its not.
Add a 250 watt mid mount motor driving the rear wheel of a bicycle with a 7 speed cassette gearset and a hub mounted 250 watt motor, eliminate the rider input via pedaling . The hub mounted motor is going to have better acceleration but its not going to have the range of the mid mounted motor since it has 7 different speed options. What happens in the situation when the bicycle with the hub mounted 250 watt motor is going to uphill? The battery is just going to deplete faster, the same happens when the bicycle with the 250 watt hub mounted motor is pushed to its legal top speed.