Why should it have a similar impact? I don't think it should.
Because otherwise the tax is regressive and effectively penalizes people for being poor. The less you have, the less you should be taxed.
And I think you're ignoring the scale of the problem.
The US median income is a little below 60,000, which is taxed at a rate of roughly 25%, based on the latest 2017 rates. The highest tax bracket is just under 40%, which requires an income of 400,000 to 500,000 depending on filing type.
Let's break that down. At 25%, the person making 60,000 will have a tax burden of 15,000, and therefore a net income of 45,000. One person can manage to survive on this moderately well. A family cannot, and that 15,000 can mean the difference between affording to pay for medication and food in the same month, or being forced to choose between them. Or it can mean being able to afford a new car when the old one dies, or being stuck riding the bus.
By comparison, someone making 400,000 with a tax bracket of 40% has a tax burden of 160,000, and a net income of 240,000. That's over five times the median income individual makes, and that 160,000 is not going to make a significant difference in their lives. At most, they'll have to downgrade the Ferrari to a Corvette, and vacation in Key West instead of the French Riviera.
Likewise that median income is not going to allow the family to buy a house, whereas the upper-income has the ability to own a primary residence and a summer house. The median income is going to find it effectively impossible to save for retirement, whereas the upper-income has investments for retirement, and quite possibly tax shelters as well, further reducing his tax burden and increasing income.
And the moment you get into the millions, the tax burden is going to be easily ignored, it will have no significant impact on the life of the millionaire. at 2,000,000, they will still be netting 1,200,000. Few people can spend that much money, and most of it will be going into investments and tax shelters that will reduce the tax burden even farther.
And by the time you get into the really big money, 10,000,000 or more, you're reaching the bracket where you can start paying politicians to pass legislation that reduced your taxes, even though you can easily afford to pay far more without the slightest noticible impact to your own life and lifestyle.
And, again, this is just Income. In real life, the overwhelming majority of the wealth of income brackets over about 1-200,000 will come from investments, aka Capital Gains, which are only taxed at 20%, cutting their tax burden almost in half, give or take.
The tax burden should absolutely have a similar impact to all people, or you're no longer looking at a society based on equality, you're looking at a society based on privilege. An equal society would greatly reduce the tax burden on lower income brackets, moderately increase it on upper income brackets, close shelters and loopholes, and bring Capital Gains rates in line with Income rates.