The torque the electric motor supplies is essentially constant irrespective of speed.
Err... True if your battery and controller can keep supplying more voltage and power.
The motor torque is proportional to the motor current. The back EMF voltage that has to be overcome is proportional to motor speed. So if you keep the torque constant, then the current is constant, and the vehicle will accelerate. You need more and more voltage to overcome the higher and higher back EMF. So the power required (voltage times current) increases steadily.
What usually happens in modern EVs is that the maximum torque stays constant up to a certain very modest speed, say 60 km/h. This is the constant torque region.
At this speed, the controller is already supplying all the voltage it can. So the controller does some tricks with the AC phase to buck the motor's magnets, thereby weakening the effective magnetic field. This is the start of the "field weakening" region. The weaker field reduces the back EMF, at the cost of lower torque. As the vehicle speeds up, more field weakening is applied. So in this region, the higher speed and lower torque come close to cancelling out, so you end up with roughly constant power. So the field weakening region is sometimes called the constant power region.
This exchange of speed at the cost of torque is exactly what a mechanical gearbox achieves, without the hassles of a gearbox. Only very high performance EVs need a mult-speed gearbox (all EVs need the fixed reduction in the final drive), and usually the performance EV's gearbox is just two speed, and needed only for Autobahn or track speeds.
The above assumes a permanent magnet motor, but much the same applies to vehicles with induction motors, such as Teslas.
