Assume you have 5000 ft extra runway past your balanced field length, your light, cool weather, everything is in your favor...you accelerate past V1 twards V2, and you get an engine fire...
Assuming you have 5,000 past a balanced field length, that number exists at V1...not after. The margin of stopping distance narrows at a non-linear rate with an increase in speed; go past V1 and the numbers are no longer meaningful.
Stopping distance is only part of the equation. Simply because one has runway ahead does not imply a successful rejection of the takeoff. Controllability, brake energy, directional issues all play a factor. An airplane at 130 knots is not the same airplane it was at 80 knots or 40 knots when it comes to getting stopped.
An engine fire is a controllable problem; one that need not merit the hazards of a high speed rejected takeoff as well. One might as well get in the air, as one is past the decision point, handle the problem effectively, and return to land stable and in control with ample runway ahead.
V1 is planned such that flying off with an engine failure or other problem is safe and controlled, whereas stopping is no longer part of the equation.
The engine is on fire continuously in normal operation. That the fire is outside the engine rather than in doesn't provide any justiifcation for abandoning plans mid-stream and entering into an unsafe condition in a state of panic. It's an engine fire. Worse case scenario, fuel chop it after getting away from the ground, and come back to land.
I don't know how many fires you've experienced outside a simulator, but my own experience has been that once the fire is detected, sit on your hands and count to ten, then address the problem with a workable cadence and some measured patience.
You're not going to try to throw in some ten tonne overgross takeoffs or disasters involving closed, dark, short runways again, are you?