Let's do the math.
Employee makes $34k, is taxed at 7%
Employee makes $36k, $34k is taxed at 7%, $2k is taxed at 20%
Now the employee works for thoe government:
Employee makes $28k -- equivalent to $34k-tax. (we're doing really rough estimates here)
Employee also does contract work at $30k. Contract work is taxed at 7%.
Employee makes $28k from government, plus an extra $6k on the side, for a total of $34k (because the tax law states that ANY earnings nullifies your non-taxable government income status) and you pay 7% tax -- and STILL come out ahead of the person who earned $36k.
So while tax bracketing inequality in the current system is indeed a myth, by introducing this new system, it would become reality. Imagine that people in Congress/Senate/etc. had this new system -- they could enjoy all sorts of non-taxable government work and supplement to the bare minimum with non-government work.
And what do you do for contractors who operate as a private entity, but are paid by the government? How about colleges etc. who get grants from the government but are private entities? How about things at the municipal government level?
There may be a place for reducing certain kinds of taxation, but every time you carve out exceptions, you create more exploitable loopholes. You have to calculate the point at which losses due to bureaucracy balance losses due to inequality. Traditionally, the US has gone for "one size fits all" -- except when it comes to corporations, who get special treatment once they can go multinational.