Other than schools on military installations, name one teacher paid by the federal government.
Sorry, Daniel, but your entire premise is just plain wrong.
The job of the federal government is described pretty well in the Preamble to the U.S. Constitution. The Constitution then goes on to detail the descriptions in the preamble.
We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America.
Establish Justice: It is the federal government's role to oversea the system of courts in the US. This begins and the local level and ends at the Supreme Court. That means local and state courts adjudicate all cases, and the federal courts should only get involved in appeals, or in federal cases.
Insure Domestic Tranquility: This is done through our system of elections. Out Constitution was written in such a way that coup de tats and insurrections can't succeed in toppling our government. Every election year the people vote, those who lose their positions to elections have no way of refusing to vacate.
Common Defense: This is done with the military. Notice it doesn't say "individual defense" or "defense of each state". There is no Consitutional backing for the idea that any policeman, military member or other federal officer is responsible for defending you or me as individuals. The role of the federal government in defense is for the entire nation.
General Welfare: This is probably the most misused and abused part of the Consitution. Just like Defense isn't about individuals, there is nothing in the Constitution that says the government is responsible or the welfare of each citizen. The General Welfare is done by the departments in government. NASA, the FBI, The Department of Defense, The Department of Energy.. etc... These departments are established to fulfill needs of the nation.
Securing the Blessings of Liberty: This part tells those who work in the federal government what the basis of their job is, and should always be.
That is the job of the federal government. Until We the People are ready to put our leaders' feet to the fire to remember it, we will continue to live under the idea that their role is anything they want it to be... and/or each of us wish it was.