> These trends seem to be present in every previous society I've ever heard of. The only method I've ever encountered was fictional and fanciful.

It's not a binary thing. Among democratic, capitalist societies (meaning leaving out other forms of government, like China's or North Korea's), there is still a lot of variation between how much the wealthy are taxed, what social services are provided by the government, how financial markets are regulated, etc. Even within US history itself, there are stark differences between the New Deal era, the post-Reagan years, the Clinton era, etc.

You can't ever really get rid of wealth and power altogether, and I think attempts to do so generally backfire and create concentrated corruption instead (see: every failed supposedly "communist" regime ever, which became authoritarian oligarchies instead). However, you can tinker with the tax burden and social services ratios.

Thankfully, we don't have to either reinvent the wheel or toy in hypotheticals. There is a huge body of research on cross-cultural, cross-society comparisons of basic services provided by different democratic, capitalist governments (infrastructure, defense, healthcare, education)... plenty of lessons to be learned by comparing Britain, the E.U., the Nordic countries, East Asia (Japan/Taiwan especially), India, etc.

The US isn't the only capitalist democracy, but there are some things that our particular take on it are particularly bad at (campaign finance, gerrymandering, privatized healthcare, privatized pipes for electricity/internet/water/etc, time-based water rights...) and others that are very much debatable (the permissiveness of free speech, journalists' rights, government transparency, mass surveillance, religiosity, guns...)

None of that requires fundamentally changing capitalism, just tweaking the regulations here and there to impact the wealthy more than the middle-lower classes (sometimes as asked for by the wealthy themselves, in the case of Buffet or Gates' calls for increased taxation).

Maybe no modern democratic, capitalist society is perfect, but some of them have solved problems better than we have (with tradeoffs, of course)... I think the most common tradeoff is that a society produces fewer extremely profitable companies & billionaires, but often the average citizen has a better quality of life (measured by life expectancy at age X, level of education, accessibility to basic services, amount of free time, disposable income on a PPP basis, consumer protections, ratio of governors to the governed, etc.) The USA is just heavily pro-billionnaire to a level that's detrimental to the rest of society. That's not inherent to capitalism necessarily, just unfettered (loosely regulated) capitalism.

> Isn't capitalism in its simplest definition just exchanging goods and services for tokens representing value?

I am not an economist, but I'll try to provide a semi-informed take. Someone please correct me if I'm wrong. AFAIK what you're describing is more the definition of a currency (and a market, in a broader sense). A market alone doesn't make capitalism. You can have a tokenized exchange of goods & services (i.e. a non-barter-based economy) in other socioeconomic systems too, whether monarchies or feudalism or fascism or authoritarian-distributive societies like China (as distinct from post-statehood communism). You can also have alternative currencies at a local level like time banks (an hour of my time for an hour of yours, rather than $s in between) and alternative local currencies (money that can only be spent within a local township/county, usually used alongside USD but at a favored exchange ratio when you "keep it local"). And of course crypto.

What differentiates "capitalism" is the differentiation of "capital" from "currency". Fundamentally, it isn't about the means of exchange (whether you trade a horse or $500 for that horse), but about ownership of the means of production: i.e., who owns the horse ranch.

It was helpful for me to think of capitalism as an evolution of previous economic systems. In the, a priest could own a temple, or a king could own everything in his empire, while a lord might own a particular area and the productivity of his peasants within it. The means of production were owned not by the laborers but by some sort of oligarchy, usually passed on by blood & marriage. Social mobility was very limited and peasants would generally not become lords.

Capitalism allowed the private ownership of the means of production, meaning farms no longer automatically belonged to lords & kings, but whosoever accumulated enough stored value (whether in dollars, gold bars, or whatever) to buy & own that farm. Then, by agreement (and often backed up by a state-enforced legal system and a monopoly on force), other actors in that society recognizes that ownership, meaning the state/king/lord can't just come in and take it without eminem domain, if other people tried to take it it would be theft, etc.

Then from that one horse farm, you can eventually save up enough stored value to buy more horse farms, maybe some railroads too to help transport feed, maybe eventually the railroad company itself, and then enough to eventually lobby/bribe the state itself and buy yourself private militias and bespoke laws made to benefit you. Social mobility was somewhat higher than under feudalism, though actual rags-to-riches stories are far and few in between. But the end point is that under this system, ownership is determined based on that recorded transaction where some store of value (currency or otherwise) is exchanged for a means of production, and that ownership is recognized within the legal framework of that society.

> One could sell one's goods or services for fair prices, take modest profits, pay suppliers and workers equitably. This would be defined as capitalism. No greed present.

This only works for a limited time, in a wild-west type marketplace where there aren't much efficiencies and consolidations. In time, usually winners gradually begin to emerge, who can then buy up all their competitors and start dictating prices and influencing laws, or create company towns or rig entire elections or outright murder people while the state looks the other way (Pinkertons, Halliburton, defense companies, etc.). At some level, one company reaps the benefit of extreme efficiencies of scale (like Amazon) while their competitors, governments, and arguably citizens/customers suffer from their unchecked power.

> Perhaps we go wrong when we fail to create or enforce rules of fairness.

Yes, and again, those "rules of fairness" already vary significantly, meaningfully, between modern, developed capitalist democracies. You can tweak taxation rates, consumer protection laws, campaign finance, liabilities (looking at you, Purdue), monopolies (infrastructure and tech), blah blah blah... all without fundamentally abandoning capitalism.

You can, of course, also go further and try to replace capitalism with something else, either more or less democratic, but it all boils down to: who controls the means of production. But if you don't account for greed and build in checks-and-balances along the way, the people who want to accumulate wealth and power WILL do so and accumulate more and more over time until nobody else is left with any. That can happen under feudalism, capitalism, fascism, corrupt "communism", etc. I'd say the answer to "how to prevent excessive greed" is more democratic than economic; at the end of the day it requires a forced transfer of wealth, sometimes willing but often not, from a privileged few "haves" to the much bigger blob of "have-nots". That can happen through regulation, taxation, violence, ethics, education, whatever... no economic system, absent an ethical and legal framework around it, will automatically accomplish that objective. There will always be bad actors, and either your system is designed to take them into account or it'll soon become their victim, no matter what you label your particular -ism.