As pointed out in other comments Tesla actually uses AC induction machines (asynchronous AC) instead of brushless machines (synchronous AC). To a first approximation an AC induction machine can produce constant torque up to a fixed speed. Above this speed the torque falls off as approximately 1/speed.

You are right about the startup torque. AC induction machines can produce full breakdown torque at zero speed, but this does require high current (but luckily not high power because the applied voltage is still low due to low motor speed).

Another limit is the junction temperature of the power semiconductors in the inverter(s). I think Tesla uses liquid cooled inverters, but this typically means there isn't much mass to act as a heatsink (relying on the liquid coolant instead), so overload times are typically very short. I'd would guess this is actually the limit in their design. In other words they can put very high currents into the motor for a long period of time before it thermally overheats, but way before that time they have to reduce the current in order to protect the power semiconductors in the inverter.