What previously existing thing, exactly, were they conserving?
...the Anti-Federalists opposed the centralized state for the purpose of what were (for the time) essentially radical ends.
Well, the Antis were led by a fellow who knew that "radical" actually meant 'getting back to the root' of something. So, yeah.
Hamilton and other Federalists wanted to keep much of the British political system intact, minus the monarch, including the British mercantilist system (central banking, Corn Laws and other tariffs).
Hamilton's goal in centralization wasn't the creation of a welfare state, it was in turning America into an industrial and military power. The debates at the time weren't pro or anti-welfare state, which didn't exist. It was a debate between agrarians vs. supporters of industrialization. Hamilton was an heir to William Pitt, not a precursor to Franklin Roosevelt or LBJ. A Social Security system or food stamps weren't on anyone's radar screen at the time, and to retroject the Great Society policies onto Hamilton and Washington is beyond absurd.