While I agree with the logic you propose in general, it is actually much simpler to take out of the right pocket to put into the left. Arguing for a simpler tax code is separate from your OP. You are asking why don't we do it a certain way. Not how do we get our system so we can do it that way. The answer to the OP is we have all the federal employees pay taxes in the same way as non federal employees because of the complexity of the tax code.
To use another item for a similar example: Fair Tax. Please I'm not putting the entire bill up for argument here. There are other threads for that. I am simply using one portion of it to show the logic. I'm sure that everyone could find parts of bad bills that they would like, even if they believe that the bill as a whole would cause more harm than good.
The logic of having a prebate instead of exempting each individual's purchases up to a certain amount (the poverty line) is the simplicity of not having to track each individual's purchases, as we do now with their incomes. If you have no exemptions but then provide the money to cover taxes on purchases, You actually eliminate a lot of paperwork and tracking.
But in the end, unless the employee really botches on their exemption status, the federal government is not really taking out those taxes. They stay in the treasury. Simply because the paperwork shows what those taxes are, the only money that physically comes out of the treasury is that from the cashed check which is the post taxed amount. In fact, if the federal employee does his exemptions correctly, the treasury will not have given out enough money to the employee.
"He who does not think himself worth saving from poverty and ignorance by his own efforts, will hardly be thought worth the efforts of anybody else." -- Frederick Douglass, Self-Made Men (1872)