I thought so too, i had that happen twice before and my controller worked fine, the 3rd time it happened i thought it would be fine, but this time the display came on but the throttle stopped working. The motor is fine, it works with another controller. I opened it up and found the shunt was a bit charred and the legs of the resistor had a bit of black char too.
The big resistor only supplies the power for thelogic side of the controller and the sensors - PAS, throttle, halls, speed. If it burns, it's normally because there's a short on the 5v somewhere, so have a close look at your throttle wiring.
For explanation, the main power goes directly to the motor phase wires. It's blocked by the MOSFETs, which are opened under the control of the CPU.
A branch is taken off the battery ones up to the LCD to power it, and when the LCD is switched on, it latches a return to the controller to power the logic side and the sensors.
The return to the controller is dropped down through the big resistor to a value suitable for the 12v regulator. The 12v regulator provides the power to switch the MOSFETs. The switching is done by transistors operating at 5v under the control of the CPU.
The 12v regulator also powers the 5v regulator, which provides the minimal power for the logic in the controller, and the main 5v for all the sensors. In total that's about 100mA.
The main capacitors just sit on the battery input to smooth it because the motor is taking power in high frequency pulses.
The shunt sits between the capacitor/s and the MOSFETs. The voltage drop across it is used to calculate and control the current going into the motor through the MOSFETs.
From that, the only way for the shunt to overheat is if current goes through it not under the control of the CPU, which is normally because of a blown MOSFET. Also it will vaporise if you reverse connect the battery.
The only ways the big resistor overheats is because of a blown 5v regulator (nothing would work) or an overload on the 5v.
Those two components are completely independent and have completely different functions.