Interesting concept, but I just need to ask for some clarification before I can consider using it for my players. Are the Exhaustion points you use disconnected from the condition Exhaustion, where you get various negative effects until death at the 6th point? If I read the last line correctly, you get 10 points and you die? If they're not regular points of exhaustion, a player can just use an action to heal themselves with a potion or spell, remove themselves from combat. Then they just need a short and long rest and they're good to go. I think this might make them too powerful in the long run. If you use regular points of Exhaustion, you suddenly raise the stakes, while still keeping the player's ability to move half movement and talk. Otherwise you're indtroducing another value to keep track of that might raise more questions than solve problems. Can they be removed with a powerful enough healing spell/potion?

Keep the system, but use regular points of Exhaustion instead. You get one action that'll really mess you up, where you are able to heal yourself, but you suffer the consequences of it after. Now that seems exciting. Just my two cents.