I'd add there are large government agencies we don't need at all. We had public education before we had a Department of Education, and would still have it if we closed that department.
Much of what the Department of Agriculture does would happen even if the department went away. Ditto the Department of Energy. Does anybody think we'd live in tents if there was no Department of Housing and Urban Development? Nonsense. The same would apply to many other departments, bureaus, agencies, and programs.
At the federal level we need a military, we need a State Department, we need border patrols and coast guards, we need a variety of serious regulatory agencies, probably more than anybody imagines without a careful survey. Somebody has to manage all the acreage and parks the federal government owns.
The federal government wouldn't go away, but it would be considerably smaller, employ many fewer bureaucrats, occupy much less office space. Some states would choose to replace certain of the lost services, others would not because some need them, while others do not. California would have an Environmental Protection Agency because they have smog issues. The Dakotas and Nebraska could likely do without, the difference being population density.
The mental exercise of thinking of federal agencies without which the nation could nicely survive is sort of fun, see what you can come up with. Go here to find the official A-Z Index of U.S. Government Departments and Agencies. I only find one of the first ten that I'd plan to keep, I figure the federal courts probably need an administrative office.