I think the issue here is around the “intended quarry”.
Whilst you might be fishing for small Perch a Pike can still take a tiny mepps or drop shot lure. I would not be confident the 3lb line Peter you suggested would survive the aggressive take of a modest Jack or bigger ..my opinion anyway.
Also as already suggested the diameter of braid is lower so it wont be like trying to cast the same strength mono it will be more balanced.
As for mouth damage, I don’t see braid being an issue on bony mouthes fsh like Pike, Zander or even Perch, plus most people are putting a trace of some sort in there anyway, they don’t tie the lure direct to the braid.
Finally as far as exhausting a fish with too long a fight …I just dont see it. Braid doesn’t exhaust a fish more than mono and even if it does the difference must be so small its unimportant. I suspect the fish is more traumatized by the hook in its mouth and being dragged from the water.