And this question comes from a country that actually has a Civil Service? Your question is a bit redundant anyway because of VAT regulation the way I know it.
You're upset I don't address all the silly problems you throw up because some government agencies in your country don't know how to keep books? That hardly is a problem that has any connections with the idea that it is nonsensical for government agencies to withhold taxes on the incomes of their employees.
I'm truly sorry that you Americans appearantly only have incompetents working for your government, but as a Dutch European I am expecting somewhat higher standards. Maybe you guys should start hire people that can figure out basic maths, because no matter which system you use with the idiots you think are working for your government it's all going to end up in a mess.