Gearboxes and battery electric vehicles

I've taken some heat for referring to the reduction gear assembly in battery electric vehicles (BEV) as a gearbox. While it is true that all production BEVs to date have used a single-speed reduction gear contained in a structure (i.e., a box with gears), the popular definition of gearbox generally seems to require gears of various ratios, able to be connected and disconnected by a shifting mechanism. Since electric motors provide little torque at high speed, little power is available for acceleration or hill climbing. One way to remedy this situation is a multi-speed gearbox, which would allow the engine to turn slower when the vehicle is at high speed, thus increasing the power available.