I noticed that champions rest for a while after they've been defeated like the sovereign does. My suggestion is to kill them off if they fall in combat.
Spells could be used to resurrect / reanimate them, so they're not a complete loss. The result of this would be that they increase slightly in value: I currently don't mind too much about throwing champions into a fight of attrition, reducing an enemy's numbers, so my sovereign can move in afterwards for the final blow. I'd personally prefer it if I thought twice about doing so - that their sacrifice actually meant something.
Effect on the economy:
1. It would encourage me to buff my champions to the max, introducing another good mana sink into the magic economy.
2. It would also mean that their items would be lost with them, which is a good reason to spend some gold to buy more.
3. Units could be raised (mana) instead of bought (gold) in a pinch.
Effect on the magic system:
Life and Death domains would get some iconic death-defying spells in their repertoire.
Edit: Quoting Malsqueak
just also have a general magic "Summon hero" spell. That way you can at least have more heroes if they die. You only get them back if you run life or death [magic].
Edit: Quoting Ausland
It could be a setting at the start of a new game whether to allow champions to get killed.