In a society where few people earned more than Nx the lowest (pick your own N), this distribution of tax origin would look very different.
Think of it a different way: suppose a government explicitly targets being able to spend 23% of GDP on government (i.e. publically) chosen goals. How does it collect 23% of GDP? Well, if everyone earned precisely the same, it would collect it equally from each person. On the other hand, if one person earned 99% of GDP and everyone else combined collectively earned the remaining 1%, then obviously the super rich person will be be paying almost all of the tax revenue themselves.
The current situation in the US is obviously not this extreme, but the thought experiment shows why it works the way it does.
Also important is the concept of marginal utility of income, which describes how each additional currency-unit of income becomes less and less significant as your total income grows.
In short, 10%-pay-80% reflects the other decisions that have been made about how the US economy works (or doesn't work), and don't have much to do with taxation in general, or the provision of public services.