I believe that a great system is useless without a culture to support it, and vice versa. A broken culture results in a de facto system that has very little to do with the official one (such as formal equality before the law being undermined by economic and social inequality). And a broken system will steadily pervert a good culture through perverse incentives.
It has been suggested that the long-livedness of institutions is the best predictor of a society's peace and prosperity. It doesn't matter that much what these institutions are: social ones, academic ones, political ones — long-running more or less functioning institutions hold together society like tree roots hold together topsoil. Remove them, and things erode.
Unfortunately, institutions are fragile. It only takes a single generation of members to pervert an institution. This can be as blatant as the overthrow of the Roman republic, or as subtle as gerrymandering and voter suppression. Systems of accountability and distributed power can be put into place to minimize the risk of an ambitious individual or cabal corrupting the institution, but such systems also tend to be seen as reducing the institution's effectiveness.
So ambitious people can be pretty disruptive to society. Often, a concentration of power in an ambitious person looks like it makes a lot of sense at the time, but it replaces a system of checks and balances with a more dictatorial one — and no guarantee that the next dictator will not be a disaster.
Humans are used to living in social groups of a few hundred people. At some level, I think we situate ourselves on a social ladder calibrated to be about that size. In modern society, nearly everyone is well aware of thousands of people who have higher status than them: celebrities, leaders, the wealthy, the famous.
Once, people measured themselves against the people in the same village: thousands of local social ladders, and most people could consider themselves to be at least not at the bottom of the heap. Now that everyone's increasingly on a single big ladder, people see the thousands or millions of people above them and something in the brain starts to scream: "you are the omega animal!" (This isn't helped by things like airbrushed models that normalize a literally impossible ideal of beauty.)
What's the fix? What's been happening, first in big cities, and now with the Internet, everywhere in the first world, is subcultures. Inside a sufficiently small subculture, even if it's global, it's once again possible to have a social context of a few hundred people, all caring about the same thing, all on the same ladder.
You might not be very wealthy or famous, globally speaking, but you can be a respected member of your subculture. Not that this is anything new. I attended a traditional Swiss cow pageant a few months ago - local farmers competing for who has the prettiest cow. I think this is an important social glue. "I may not have as much land as the farmer next door, but I have the prettiest cow in the village" may sound silly to you, but if we translate it into "I may not earn as much as my friend, but I (am a better cook, programmer, spouse, football player, environmentalist, churchgoer, GM, singer, etc.)" — that's the kind of thought you have probably thought.
In short, having few measures of status, especially ones that are so destructive to acquire as political power or money, is very bad for a society.
My suggestion, then, is to encourage a culture that rewards time invested into anything other than power and money: culture, science, sports, engineering, art — with a cheerful lack of discrimination. Passion matters, not the topic. Literature, raising pretty cows and well-executed cosplay are equally noteworthy achievements. In fact, surplus productivity is channelled into celebrating these achievements. On the other hand, accumulating large amounts of wealth and attempting to hold on to power long-term are disdained. Taxes rise steeply, terms are limited, David's sortition-election system is used to put people into power. There must be no awards, limousines or TV appearances for the powerful — but raise a pretty cow, and the nation applauds.
(The question of how to get from here to there is left as an exercise to the reader.)