Well, I have tested it in other games, like Romance of the Three Kingdoms. That game has a limited number of officers in it. Now, as the time line priogresses, there are children "born" as they historically, would, but there is a finite number of champions. These officers can be killed in a number of ways, they can be killed in battle, duels, or beheaded when captured. One of the best strategies to win, although not terribly fun, was to capture and execute as many officers as you could. This can greatly depopulate the game, and in some versions of the game, can leave you unable to "win" but leave you no resistance.
If there are few champions in the game, having them killable certainly makes them precious, but almost so precious that you don't even want to put them in harms way. If you make them killable, but high in numbers, they just become another generic troop. If they are high in numbers, but unkillable, they replace armies entirely.
Now low in numbers, but unkillable is the best solution. They are rare, but not so precious that you are afraid to actually use them. they are few, so they support armies instead of being the armies. Also, the game, no matter how long you play (and some of us nerds have super long huge games) will be in the game.
Now, the dynasty system is no longer in the game, so there is no way to "replenish" our supplies of champions. So with a set number of heroes, it is my strong belief that a low number of interesting and unkillable champions is the best way to go.