We didn't take care of Saddam Hussein the first time we were in Iraq because it was outside of the UN mandate for the operation, and we were invading with troops on line next to US troops who would have thought nothing of turning the turrets of their T-72s 90 degrees left or right and engaging US Forces (Syrian) had we crossed that line.

The Syrian Monarchy has never been a friend of the US, merely an ally of convenience during DS because Iraq was as much a threat to Syria as anyone else. Both sides play that game, and have for aeons, as "The enemy of my enemy is my friend"

The US sold Iraq conventional weapons during the early 1980's while they were fighting Iran as a counterbalance to Iranian power. During the 1970's we sold arms to Iran for the same reasons, so there was a counterweight to growing Iraqi power. Geopolitics is ugly, and makes for strange and temporary alliances.