Who wants to be in the business of busing children to school? The government is not in the business of competing with private enterprise and in the few cases it does is because the people demanded the government provide those services.
THAT'S the correct question. It is to prevent that sort of government effect that the government "taxes itself" presently under the income tax or under any of the flat tax plans proposed and there is certainly no rational reason why government output should be excluded from the FairTax base.
If you did some looking into the matter, you'd also find that most economists also have the view that including government output in the tax base is proper.