I agree in spirit with what you say and would, in an ideal world, like a flat tax rate for all but the problem is how to ensure that pay is distributed fairly? I don't mind a director at Barclays being paid 20 or 30 times a cashier in one of the branches but when it starts becoming 100 and 200 hundred times more you can no longer start accusing those at the bottom simply of jealousy as there is a genuine and legitimate feeling of unfairness.
Then look at how jobs and wages are decided at each end of the scale. It seems to be people at the top are given pay rises to make them work harder, whereas people at the bottom get there job threatened to motivate them. This is a well known and generally accepted unfairness built into our corporate culture.
If the amount everyone was paid was truly meritocratic and same market forces applied to the top and the bottom of the job market, a flat income tax rate would work. But we're no where near that kind of culture.