The biggest limitations are thermal, not electrical.
Practical electric traction systems can't actual do full torque at zero rpm (because at zero rpm, you're only using two legs of the inverter, not all three, so thermal limits are significantly reduced). However, once turning, at anything more than about 100rpm, full torque is available, if the motor and inverter are cool enough.
At low speed and cold (speed = power, because of the fixed drive ratio as no multispeed gearbox is fitted), the inverter output current limit is the, er limit, and motor torque will be maximum (Torque is proportional to phase current). As speed increases, and the voltage ratio between the DClink (battery supply voltage) and Phase voltage falls, battery current increases, and at some point, the battery power limit is hit. In conjunction with this, the motor will reach a speed where it's back emf equals the supply voltage, and in order to keep turning faster, a technique called field weakening is used (this uses a deliberately miss aligned (ie offset from the quadrature axis) phase voltage application to squash some of the magnetic field in the air gap, which reduces KE, and hence allows the motor to spin faster for a given DClink voltage. However, as you are now using some of your phase current to reduce KE, you loose some torque capability, so the motors power is also limited. In this field weakening region, (typically 2x basic DClink/KE region) motor power falls slowly with speed increase. (demag limitations must be observed). Ultimately, the motors phase inductance finally limits the power output (assuming battery power > motor power) as the motor is turning too fast for the applied voltage to push enough current through the windings in the time available.
For an EV without a multispeed transmission (most of them, for cost reasons) there is a trade off in the gear ratio chosen between the traction motor and the wheels, and hence the lowest road speed at which the system can make peak power. In something like a Tesla, which is expensive, they use a very over-specified inverter to be able to push massive current through the motor (when it's cold) at low speed, to make up for the lack of gears. Cheaper EVs don't have that luxury, and performance from zero speed is typically below that of an ICE powertrain (something like a Leaf, or I3 really only accelerates well above about 20mph, rather than from 0mph)
Typically, peak power falls at around 50 to 60mph, and above that, power is constant, as limited by the battery and field weakening capability of the Emachine.
Take a look at the Tesla inverter:
that is NOT a cheap device!!
But as i said, it's the battery, inverter and motor thermal performance that sets the limits really. This is especially true of the peak power condition, where rotor heating becomes accute, due to the addition of iron losses (eddy current driven) to the copper losses (P=I^2.R) in the stator. On the Emachine i developed for the Mclaren P1 (~24kg / 200kW in FormulaE spec) we used a internal water cooled rotor, and had to get a stream of cooling water into, and back out of, the spinning rotor at up to 20krpm! I have quite a few grey hairs to show for it too......