"The three legendary leaders are Napoleon, Wellington and Blucher. If they are leading from the front, there is a small but non-zero chance that they could be killed by the enemy. If that happens the battle instantly stops and the whole army routs"

I'm not sure an entire army would rout if either of these three leaders were killed. Only a small section of the army would see this happen. Also, would Wellington's army have turned and run if a stray shot killed him in the late evening when the French army itself was leaving the field?