Could America defeat the rest of the world if no nuclear weapons were allowed?

If we wanted to? Likely yes. The amount of arms and their capabilities is pretty top notch. However The US hasn't tried or wanted to win a war in a long, long time. That isn't the purpose anymore. With Military-industrial complex we have in place victory isn't the prime objective. The wars themselves are the prime objective and by and large the motivation is to keep the war going in the name of arms profits. But on the same token there are few countries that can match our military hardware and expertise and of the two that do have comparable and in few examples better hardware we spend and stockpile so much more.