The countries that do well not bothering are usually the ones without the power or reach to make it work, or not in the right geopolitical situation.Quite a few countries seem to do well enough without going out to destabilise or topple overseas rulers, or install dictators. It's not a battle of necessity: the US has economic power and security quite enough without this stuff.
Denmark doesn't need to. Denmark meets the vast majority of its needs through the EU which is full of stable countries operating a system of mutual advantage, which vastly reduces the need to screw with ones neighbours (Although even then, if memory serves me back in the 80s the French government was bribing German politicians.) Canada is vastly tied to the USA, and effectively piggybacks off any advantage the USA achieves because the trade flows so freely over the border, so it doesn't need to do much itself.
However, countries which have lots of antagonistic opponents and/or significant interests in unstable parts of the world are much more likely to benefit. The Middle East is an obvious example: at least four major regional players (Turkey, Israel, Saudi Arabia, Iran) plus global players, full of religious and ethnic instability and an incredibly vital resource. For the USA to stand back is effectively for the USA to concede influence over a lot of these places. It doesn't matter how much the USA makes the people of Ruritania love the USA if Russia strongarms a brutal dictator into control of Ruritania, who then trades exclusively with Russia for Russia's gain and the USA's loss.
I am intensely aware of the tension between defending the rationale for interference in other countries' affairs, despite deploring the frequent results. I think these are very difficult questions in the world, where morality and practicality don't necessarily gel very well. My ethos is perhaps "enlightened self interest": try not to fuck with people, but if you have to for your own good, try to be as gentle as possible. And remember to feel bad about it, so you carry on that way.
Thus I'd rather have the USA that looks at the wreckage it has wrought and asks itself "Guys, did we do a bad thing here?", than other regimes that would spread destruction and misery and just have a congratulatory wank over a job well done. The USA is much more likely to exercise restraint.