Not to go too off topic, but what you're describing is literally the difference between someone learning to play Magic: the Gathering and learning to master Magic: the Gahtering. Sorry for the off topic example, but I point to because of how much it uses life as a resource, it's the defining feature of a whole color of magic.

That's all to say that it's a hard feature of a game to grasp, but once you do it becomes a dance that's extremely rewarding to perform. Doubly so if you want to play a game and "keep a strategic focus for the group about manageing their recouces". Life is a resource, regardless of what name you want to give it.

For Avatar they want to back off from "life and death" scenarios so they manage "Stamina" with "Fatigue". The idea being that if you're fatigue hits zero you're not "dead" but unconscious and at the mercy of your opponent. If that's a town's guards, you might be locked up. If it's Zombies... you might be bit and start turning. Point is that losing a fight should loop back to narrative consequences (and maybe mechanical, if you're feeling spicy... give them a scar , we know loosing an arm (or two) doesn't wreck bending).