Extrajudicial targeted assassinations are pretty far on the bad side, no matter how few other people get killed in the process.
Sure, if you are doing it, killing fewer bystanders is preferable on the surface. But if individual assassinations are less likely to cause an international outcry since fewer people died that likely leads to more assassinations.
Well that's the thing... None of the superpowers are actually at war with anyone there.
It's mainly a local conflict with the superpowers backing different factions. Kind of like a proxy war during the cold war. A lot of countries backing opposing local factions while trying not to escalate.
A full blown declaration of war would give us WWIII in no time due to it being such a complex mess of alliances they're.
With whom exactly? With Syria? Then why have the Congress never declared war on it? With some terrorists who happen to be in Syria? Then why is the US fighting them there, not the Syrian government? What's that? The Syrian government is actually fighting them too but demands the US forces to leave the Syrian territory, which demand the US ignores because why wouldn't it? It can't be declared to be engaging in a non-provoked aggression against a sovereign state since it has veto in the UNSC, after all.
The US is not at war in Syria. ISIS is deemed to be a threat to stable governments in the area including Israel, Iraq, and even Turkey, and US is assisting those governments in fighting ISIS back. The seemingly endless civil war in Syria is still a civil war although US had at one point been supporting certain groups.
My idea was that the US is fulfilling the ally obligations towards these governments. ISIS itself is not a recognized sovereign, so it cannot be declared a war to, thus no congressional approval.