Before we get to my answer, we must first acknowledge that anyone’s answer to this question will be influenced by their backgrounds and their political beliefs. I grew up in what could be called the Third World, but I was an American citizen and enjoyed essentially a First World lifestyle even then. This may color my judgment and make me more pro-United States than another person might be.
My view of this is that the question sets up a false dichotomy. It implies that the US might be the cause of global problems or it might be working to solve them. It implies that one or the other of these must be true and that they cannot both be true at the same time. It also implies that there is no third option.
I would support a third option. I would say that the US and other First World countries are not the sole cause of global problems. I would say that global problems are the inevitable result of human nature and that there have always been global problems. The strong have always caused problems for the weak. This was true when the strong were the Mongols causing problems for the Europeans and the Muslims. It was true when the strong were the European countries causing problems for Africa. It was true when the strong (in at least one area) were the Japanese, causing problems for China, Taiwan, and Korea. Whenever some people are strong and others are weak, problems arise. This appears to happen regardless of the type of governmental or economic system that the strong believe in. So, I would say that the US and the other First World countries do “cause” global problems, but not because they are especially evil. Instead, whatever country is strong will cause problems for the other countries.
In addition, I would say that the US tries to rectify the problems that it helps to cause. You can say that its efforts to help are insufficient because the US will not give up its power and its capitalist system. Nonetheless, the US and other rich countries do try hard to fix at least some of the problems that they help to create.
So, I would make two main points here. First, the US helps to cause problems, but it also tries to remedy them. Second, we should not conclude that destroying the US would put an end to the problems. Whichever country became strong in the wake of the destruction of the US would cause problems as well.