People underestimate the impact of the US on the stability of the modern world.
I don't think they do, it's pretty well-known. You even used that phase 'when the US sneezes the world catches a cold' - that phrase wouldn't exist if people actually did underestimate the impact of the US on global stability.
Has the US screwed up a few countries a few times, sure. Iran, certain Latin American nations, Afghanistan are not the best examples.
But compare the peace across the majority of the world since 1945 vs the constant European and Colonial Wars of the 17th, 18th and 19th Centuries.
This is purely down to the US as a Super Power, and their drive to encourage Democracies, especially post WW2 in Europe.
Admittely the Cold War played its part, but it was a Cold War of Democracy vs Communism, and US was the standard bearer for Democracy.
I think that's ridiculous. The 'Pax Americana' is real, just as the 'Pax Britannica' was real - dominant powers tend to do that, and unipolar systems tend to be more peaceful than multipolar ones. In that you're correct. However, the 'peace' we see between major powers is overwhelmingly a result of the threat posed by nuclear weapons. Without nuclear weapons, there would've been conventional wars between great powers on multiple occasions - the Soviet Union would've pressed its advantage in conventional arms pretty early on. Even now, it would probably do well in a confrontation in the Baltic.
You mention democracy - this is Francis Fukuyama's point, that democracies don't fight each other. Well, there's probably something to that but we do have limited data from non-nuclear ages. However, to insist that the US 'spreads democracy' is laughable in the extreme. The US had been an agent of authoritarianism, preferring to topple democratically elected governments in favour of strong man dictators friendly to it. The US's record has not been good in this regard, and even the 'democracies' that it has attempted to install have been very fragile, except those created in the aftermath of the Second World War.
Because of the US for the better part of 100 years, the idea of how to be rich and successful in the world was - Democratic elections, a free capitalist economy and a free press that could report the truth.
Compare that to the pre-WW2 where the press and freedoms wererestrcited, and post WW2 Authoritarian regimes such as Russia and China.
If you are the wrong person in these countries, you disappear. The wrong ethnic group, the wrong religion, the wrong sexual orientation, you are targetted and removed.
The press is restricted (and in recent times, the Doctor that discovered the Corona Virus was silenced by the Chinese government, allowing to spread further... extremely stupid).
Despite all of its faults, the fact we live in a world as free as it is is down entirely to the US.
I don't know why you think these things are a uniquely American legacy. The US inherited this cultural legacy from the British and the French, and American 'democracy' is profoundly oligarchic as it is.
If the US falls, expect more regional wars, more violence, more refugees and the slow death of Democracy. New Tyrants will rise and the enlightment will be nothing but a memory.
Don't forget, in 1984 shows us a world of unrestricted Tyrants messing with history, believe me we do not want that.
The US is falling, and there'll reach a point when China and Russia will feel safe enough to start their own wars without American interference. Russia has been testing the waters for a while now, and is almost at the point of acting with impunity. Both of these powers have security council vetoes, so the UN won't mean a damn thing, and in that case NATO is absolutely key (which is why Trump's original policy of 'fuck NATO, America first', which he's completely u-turned on, was so disastrous for the West).
