There's a good podcast about the evolution of US income tax: https://99percentinvisible.org/episode/624-tax/
EDIT: So supposedly in 2021 Musk paid $12B in taxes (which was an anomaly) and in most years he pays around 455 million federal taxes. There was one year where he took no income and paid no taxes. So the average American probably pays ~10K I would imagine.
I agree with your intuition, but this is often contested based on the idea that one of the state's services is protecting property, which scales up in cost in some way with the amount of property.
For example, if you have a 10-story building, the cost of protecting it against fire is greater than the cost of protecting a small shack against fire (the kinds of fires it can be involved in and the means of accessing it to fight them are greater).
Or, if you have valuable jewels, the cost of protecting them against theft is greater than the cost of protecting a few items of clothing (more sophisticated attackers like organized crime and otherwise professional criminals may try to steal them using more sophisticated means and resources).
Or, if you own corporations, the cost of protecting your ownership interest against fraudulent transfers may be greater than the cost of protecting someone's ownership interest in a house against such fraud, again because of more sophisticated attackers and also because the rules permitting transfers of the corporate ownership interest may be more complex to formulate and apply.
However, it's likely that the cost of protecting most kinds of property scales sublinearly with the economic value of the property rather than superlinearly, so if people were merely being charged for the increased cost of actually providing them state services that they use or directly benefit from, this would still not justify tax rates increasing with wealth or with income.
I wish I could pay taxes at a rate of 0.25%! What tax rate did you pay last year?
We tax capital gains less because we want people to invest their money in companies. As I said, we can debate the tax rates, some might argue we should lower the tax on capital gains (double taxation?) some might argue we should raise it. We should absolutely have an evidence based rational discussion on these topics.