I like the idea of using war desire as a way to press demands, and as a stand-in for the stale "casus belli" mechanics that many 4X games have been leaning towards recently. It's a fresh approach to this that does a cool job of capturing the idea that a government needs popular support and justification in order to go to war, and that those things build up over time. However, I really don't like using war desire as the currency for resolving wars for a variety of reasons:

  1. From an immersion perspective, your people's willingness to be at war is not what should determine how much your opponent is willing to cede to you by surrendering. That just doesn't make sense at all. 
  2. From an "is it fun?" perspective, the war desire system as it is currently implemented has left me feeling unsatisfied at the end of every single war that I fought in my many playthroughs. It felt like I was utterly spanking the AI only to be able to press a couple of my demands, because the war desire maximum seemed to be capped at like 200 or something. 
  3. Taking it back to the immersion perspective again: I would often occupy territories that I also had culturally and religiously dominated, that were a part of the demands that led us to go to war... only to be forced by the war desire system to give those territories back to the AI upon forcing them to surrender. That makes absolutely no sense. 
Suggestion: The war resolution currency should be seperate from war desire. I think that war desire is a great currency to determine whether my people support me going to war, and to determine whether my people support me staying at war (so if the war desire falls too low, I should start to see stability issues, etc. in my cities), but there should be a seperate war score that accumulates over time based on battles won, territories occupied, etc. to determine which demands I am able to press at the end.