I can only really see war exhaustion directly superseding an empire's decision making autonomy (as a player) if it's something like planetary unrest (but planets already rebel under sufficient unrest in aurora) or loss of crew. I don't see this ending conflicts directly though, at most they should be formed as secondary effects (loss of military academy efficiency due to sending crew to meatgrinder) as there are many wars that you obviously should not be outright surrendering regardless of the war fatigue, unless it's one where all faculties for your empire to control it's assets are voided. See: just about every spoiler race, and alien empires who would obviously force you into peace specifically for discretely parking a fleet of missile carrying ships to alpha strike your home planet.
As is, we already know that PPV isn't representative of lost war value... It's minerals to construct a given ship, it's crew training, the inverse of it's current maintenance clock, it's commanding officers, and the opportunity cost of the slipway/shipyard size/maintenance capacity to build it and keep it going.
As aurora is now, the diplomatic stance you have available is "ready to wage war at any moment", and adding in exhaustion mechanics that make it so you can't fire missiles you have loaded in magazines once an ephemeral diplomatic threshold is passed is honestly not a good idea, in my opinion. That said, we can make the AI find peace much more palatable if they've burned through their officer pool and have to use untrained conscripts on their vessels. Players might be kind to that idea as well. Though, naval academies would likely have to be re-balanced to have diminishing returns, and to partially scale with planetary population and "officers died in combat" fatigue maybe, as the current system feels a bit too feast-or-famine by design... I've never actually run short of officers before running short of minerals, ever.