My second point is mostly that players' actions would be constrained to the point where they won't have any ability to not start a war while still having fun. Only having one political "hit point" before all-out war means that there's very little middle ground between playing excrutiatingly safe and saying "screw it, let's start a war", so players may feel railroaded into one of the two approaches. Having a cushion means that players have more ability to sacrifice portions of their safety net for specific objectives- they might be able to steal an artifact, but at the cost of food rationing and forced conscription as the city gears up for war.

What sorts of adventures do you envision the players going on (pre-war, that is)?