You're missing the point: You wrote that "The government does not tax GDP." It does. Also, anything that the gov't spends then counts as income for the other

You're missing the point: You wrote that "The government does not tax GDP." It does. Also, anything that the gov't spends then counts as income for the other party = more income for the gov't. It is why debt-to-GDP is a very important ratio. It is also why the PIIGS were obvious candidates for financial meltdowns.