Your calculation is not correct for several reasons:
Firstly, your battery voltage drops pretty rapidly initially, so the 71.4v is not realistic. You'd probably lose one or two volts before you could draw any meaningful power from it.
Secondly, you get voltage sag. The battery voltage goes down in proportion to how much current you take from it. I can imagine losing 6v at 60 amps. This would mean about 64v when you fully open the throttle, which would be 3840w from the battery,
but thirdly there is a switching loss of about 5% in the controller, which takes it down to 3648w.
Fourthly, the back emf from the motor reduces the current going through it in proportion to speed. At zero speed, there is no back emf. At max speed, the back emf blocks all the current. Basically, you only get the max current at low speed. If you used a wattmeter, you'd see how much power was coming out of the battery at at any time.