If the US stayed out of other countries politics and there were no coups or installation of people favorable to the US what would the world look like?

The US projects its own interests worldwide but those often overlap with the interests of other as well.

For example, the US often stipulates intellectual property and worker rights in it's trade deals. The US actively protects shipping lanes. The US actively negotiates visa-free entry for American passport holders to other countries. The US invests in the economies of foreign countries to stimulate trade opportunities. The US controls the SWIFT banking network which makes it so that we don't need to send gold bullion or pallets of cash to buy things from other countries, and participating in the system requires member countries to have certain controls in place that attempt to block bad actors. The US, through it's embassies and ambassadors, deploys it ideology to foreign governments, and makes deals that allow foreigners to invest in the USA and Americans to open businesses in foreign countries.

The US actively shuns and makes life difficult for menace dictatorships on the global stage by creating trade exclusions.

There have been coups since the beginning of time and always will be, as it's human nature. Many citizens of other countries have no belief that the future of their country belongs to them after decades or centuries of dictatorships or kingdoms. On the whole, history shows that kingdoms rise and fall for many reasons and the people sometimes benefit and sometimes suffer for it.

Obviously it's a highly complex topic, but if the US wasn't doing these things, then Russia or China would be, or there would be more powerful regional factions, which could reduce the size of the world in terms of travel and trade options for many.

Whether the US is the right one to be in control of this at this point in history is a matter of intense debate among some, but it could absolutely be worse than it is now.