Using a x-speed transmission with a DC motor
There should be no advantage to a transmission with a variable ratio like the gearbox in cars. With current technology, electric motors with electronic speed controllers can provide a sufficient range of speed adjustment for most vehicles.

There may be a need for a fixed-ratio gear to match the electric motor drive system to the vehicle.

If there is something preventing the best design from being used for the electric motor drive system, a variable-ratio transmission could compensate for that. There may also be some unusual vehicle requirement that could benefit from a variable-ratio transmission.

Mechanical transmissions have the advantage of providing pretty-much constant power at any selected speed. The disadvantages are some wasted power due to gear friction, increased drive-train mass and volume, and added maintenance requirements.