TX teaches what it wants now, so does FL.You're ignoring the pork. If the DOE wasn't there, States like Texas would stop teaching anything but completely varnished views of history for example. Literature would be added to "what do you need to learn that for"?
Better to increase revenues by getting rid of the caps on SS and the federal sales tax you mentioned.
But you are correct that Federal money has "strings".
Columbus Day is now "Indigenous People Day"??????
But your point is a good one. Cutting spending is not a cure, more revenue is.