You know, Paradox could always try something radical, like integrating War Exhaustion into their existing system of citizen factions. Each faction type as different goals in war; the materialists want more shit, the authoritarians want more worlds, the militarists want to win, the xenophiles want their border to be left the fuck alone, egalitarians want to end oppression, pacifists want he war to be over, and spiritualists want whatever the great space god tells them to want.
Each faction could contribute to the war exhaustion based on their goal in the war. You're capturing lots of nice systems with plenty of resources? Materialists aren't going to complain, hell, throw in a strategic resource and they may even roll it back a bit. However, the pacifists are going to be upset as all hell that you're embarking on a war seemingly with the intention of just raiding resources from your neighbors, and the authoritarians aren't going to be impressed unless there was an actual world conquered in those resource rich systems.
Scale these effects by how many pops you have of any particular ethos, and bam, it's almost an organic system. If you're in a war and you just need a little bit longer, you can use faction suppression to cut down the influence of the peaceniks, or to encourage the militarists who approve of you trucking across the system and showing the enemy fleets whose boss even if you don't actually conquer ground.