The US government doesn’t run in the way they are acting like it does. The executive branch exists to execute laws as written by congress; it’s in the name. If congress passed no laws the president would have nothing to do besides negotiate with other foreign heads of state and be commander in chief. Most of what DOGE is cutting has been legislated. Which is not something allowed to be done by president or the executive branch. Of course they can make the case to congress that certain agencies shouldn’t exist, and pass laws removing or defunding them. Or they could pass a law giving DOGE powers.
Of course there are modern legal theories which disagree with what I’ve said above. However they are modern, untested, and largely ahistorical.