I believe people should ideally pay the same for the same citizenship benefits but I also realize that is impossible. However, if the top one percent makes 20% of the income they certainly shouldn't pay more than 20% of the income tax and all of the estate tax
You see there is no logic in that stance. The whole idea of a country/state/town/other similar entity, is burden and the improvement of all over time.
In your example we have 3 people and a 20% flat tax rate.
Person 1 earns 100 dollars. That leaves them 80 dollars for food and housing which costs lets say 70 dollars minimum.
Person 2 earns 1000 dollars. That leaves 800 dollars for food and housing which still costs 70 dollars minimum. Yes they can afford more fancy housing.
Person 3 earns 10000 dollars. That leaves 8000 dollars for food and housing which still costs 70 dollars minimum. Yes they can afford more fancy housing.
Total tax collected is 2220 dollars.
Now the burden on person 1 is massive, compared to the 2 others. Person 1 does not have much wiggle room and certainly needs help and luck to move up in the world.
Now how about we did this instead.
Person 1 still earns 100 dollars, but his tax is now 5% instead. So he has 95 dollars left, 70 for food and housing and now he can go to night school for a better education.
Person 2 still earns 1000 dollars, and his tax rate can be lowered to 15%. He now has a tad more money but in the whole scheme of things it is pretty irrelevant.
Person 3 still earns 10000, but his tax rate is now 30%, which still leaves him 7000 dollars to play with... more than enough for food, education, housing.
Total tax collected 3030 dollars.
So you have a larger tax income to pay for the education or help to person 1 and sooner or later, person 1 moves up to person 2 tax bracket or even person 3. That would certainly almost never happen in your example, since the economic restraints of person 1 is so bad that missing a pay check would put them out on the street.
Point is, if you want to live in a society where anyone can be anything, then you have to "rig the system" to make it so, else you become Victorian England or worse, where it is more important where you were born and who your parents were, than your skills in general.
So what if the top 1% pay more than 20% of the taxes, they also earn far far more than most and can easily afford it.