According to the tooltips, the only difference between Militia, Soldiers, and Elite Soldiers is health. They all do the same damage (though ES have 5% more "to hit" whatever that means) - they only cost more.
So a battle where you go in with 100 recruits and 100 militia losing 99 recruits would still lose 99 recruits if you went in with 100/100 ES.
Given this, why would you EVER use ES except in a battle where you are losing them? Do such battles exist? Everything I've seen has been centered around losing recruits if possible, militia if profitable, and soldiers if you must. Show me the battles where loss of ES is a profitable idea.