Hmm...
Folks deconstructing the 'failure' of Gulf I that left Saddam in charge often come back to "our Arab allies wouldn't have supported his removal." True. But the French, Brits, Italians, Turks, Aussies, Canadians, Danes, Dutch, etc etc would have.
Would they? I seem to recall at the time talk that they wouldn't. And I don't recall any of them being particularly critical of Bush I for not removing Hussein. But I'm probably wrong---I wasn't following closely.
On the other hand, I don't know that we could have
not intervened in Kuwait. But removing Hussein when we did does not seem to have gone very well. Sure, he was a horrible dictator, but he was a secular dictator. (One suspects that is part of the reason those Arab allies didn't want him removed.)
As to the rest of your concerns, as you say, the Chinese, the Russians, the Iranians, the Martians, or Shadow Host of Middle Earth aren't stupid. I don't think they needed the demonstration that given a target, we can hit it. Or that the US's weaknesses involve internal politics.