I agree with you on the should part. The problem is that with more power and more population, the nature of the issues you face domestically and across the world become harder to have a solution for.
Imagine being responsible for just yourself. Now a small town with a population of 10, then 100, a thousand, ten thousand, a hundred thousand, one million, one hundred million...
It's pretty easy to look after yourself. Ten people? Still pretty trivial to divide tasks. I've had a role where I was responsible for the welfare of nearly 300 people... almost an impossible task if it weren't for delegation. Even just being a teaching assistant in graduate school, I had 1,000 students and pretty much all I did was answer e-mails and grade papers, but around exam time it was overwhelming keeping track of the myriad of excuses and following through with them.
Running a country with 340 million people? Many of whom don't speak English, or don't follow the law, or don't pay their taxes. All the while maintaining a global military hegemony, with nations around the world depending on you for providing security to international trade routes and disputed borders. Leaders at all levels have conflicting ideas about how to prioritize funding, how to behave internationally, how to look after the citizens, the tourists, the foreign workers, etc., and a population that has an even wider view.
Nowhere in human history has increased power and wealth translated into a utopia, because the resources simply don't exist to cover all the bases. I can only think of examples where an empire encountered more problems as they grew. The benchmarks for social welfare and humane policy almost always come from homogeneous societies or small economies for a reason.
A big issue is that it's harder to oversee the process when you work towards a solution... from the steps of capital hill to the line at the soup kitchen, there's always someone lining their pockets, sometimes at every step down the ladder. The logistics involved in moving everything from point A-B and point AAH-JPB is an incredible issue on its own.
Should we do better? Absolutely. Can we? A little. Will we? Depends on what your personal priorities are.
My two cents, at least. I don't claim to be the smartest person in the world, and you can have a different viewpoint that conflicts with mine and is still perfectly valid.