"running away was futile" - I don't believe that for a second. Of course most casualties happened during pursuit, but that's not the way to look at it if you are a soldier on the losing side of a battle. In fact most soldiers who rout could survive and that would not contradict the statement "most casualties happen during rout"...
From the perspective of a common soldier, once the battle goes badly and the enemy starts to get into your line's rear, he has to consider where he is more likely to die - in the failing battle line, with his officers (who unlike him will can surrender to the enemy and expect to be treated well), or on the road / in the hills / in the forests away from the enemy sabers and lances. The decision to bail and run would in most cases be the better decision.
"Often quite futile" and comparable to the chance of escape when running from mechanized troops in modern combat was the point I was trying to make.
As for running being the better decision it could certainly be true in many situations, especially if there is danger of being encircled. However, in the slow shoving matches of ancient battles a soldier would be more likely to survive a losing battle if his unit stayed in formation and fought on until nightfall rather than if everyone made a run for it. Once the army started to rout it was of course wise to join in .