Box, the US has been 'technically' *at war* with Korea via th UN. It is just not true to say that the United States is 'in* a state of war' with Korea today.
There is a very big difference between situation with Korea & Gulf today your statement just doesn't wash.
In KOREA even the 'current 'technical' state of war was sanctioned by the UN, also Gulf-1 was an alliance sanctioned by the UN. Gulf-2 is being opposed (at present due to lack of evidence to justify an invasion) by the same UN.
YOU CAN'T HAVE IT BOTH WAYS. UN has *not* yet approved an invasion. But UN support was good enough for Gulf-1.
Cheers
Doug