Electric power is well suited to driving the huge wheels of a 4x4 monster truck, great low end torque and wide power band. The problem might be battery weight - monster trucks are basically lightweight space frames with low unsprung weight pushed by a big block V8 engine with a flimsy fiberglass body over the top of it all.
With how massive the wheels and tires are, maybe hub motors with batteries packed in their centers could work. I don't get the impression that monster trucks strive to minimize unsprung weight, the tires are wrecking balls.
You wouldn't need huge battery life for a 15 minute performance, so shaving off battery weight might just work. What most people go to see is airborne jumps rather than crushing things hence need for low weight.
IIRC the rubber tires weigh 1000+lbs each, I wonder if the tires could be implemented differently using lightweight materials shifting their weight budget into hubmotor+battery.