The world? Probably not much different than it has over the years. The real question is whether America will allow herself to be ruled by the world or to be an independent leader/partner.
For all her faults, impoverished countries, countries hit by disasters, and small countries up against attackers have been given a helping hand by Americans. If America continues the decline she's been in her help to the world cannot continue on the same scale.
There are naysayers focusing on her failures, but it is a wonderful study to research the truth about the dollars/subsidies, the food/medicines, the manpower/defense America has offered countries who ultimately turn on her, mock her, and do all they can to degrade her. They are also doing that to themselves in the process, of course, but the truth is still the truth.
Comparing how America has reached out to try to help other countries with what others have done to help is another facet of such a study that gives real insight. Again, there will be naysayers pointing out failures, but really, there is not much comparison. What those countries' leadership have themselves done with that help is in some cases worse than appalling. That's another study worth doing.
The world? America needs to focus on an introspective review of how she has come to the place she is at and make decisions that are not easy, that will require some sacrifice and hard work, and which include examining the integrity of her values if she is to be great again and build a country for future generations.
Though she is filled with those who mean to prevent that effort, if she will take stock and go to work what the world will think is that they are grateful someone stood firm while they crumbled and, therefore, they again have help from America (though it will take longer than the next few years to regain the lost ground she needs to work toward).
Even if the world never comes to appreciate America again it is far more important for her to have the self-respect that comes from trying to hold the line on what is good in as many areas as possible. If she will make the effort and do the needed work she can have true self-respect that will allow her to continue forward instead of continue to decline.