One of the reasons Edmund Burke gave for his opposition to the French Revolution was the increasingly anarchic tendencies of the Revolutionaries. He correctly saw the conflict between radicals and conservatives as one between those who want to tear down social order and those who want to maintain and restore it. By Burkean standards, the advocates of limited government in post-Revolutionary America were the radicals, while the Federalists were the conservatives.
Nor did anyone consider the bomb-throwing anarchists "conservative" a century later, even though they too advocated limited government. The false equation of big government = liberal, small government = conservative is basically an artifact of modern day America, where the power of the Federal government is being used solely to achieve radical aims. If the Supreme Court ruled to outlaw abortion nationwide rather than to legalize it, would conservative advocates of small government attack this on principle as federal overreach?
Burke's support for the American Revolution was nice to have but the revolution would occur in any event with or without him. Jefferson's Declaration of Independence adopted unanimously by the thirteen colonies is by far the better guide to our revolutionary principles. After two terms of national icon George Washington and one of John Adams (who did not much care for Hamilton), the voting public put a reasonably prot end to Mr. Hamilton's upper class, elitist. know-it-all Federalist Party and, by electing Jefferson, Madison and Monroe to six terms, reclaimed their heritage and our country.
Our revolution was based on a refusal to be governed and abused by an arrogant royalist elite in England. When you call Federalists "conservatives," you are suggesting that tyranny by an American elite was OK and that the peasants had better get used to it. Actual conservatives will tell you that such an American tyranny of, by and for bankers and manufacturing elites and landed gentry just won't do: then, now and forever.
Burr put Hamilton out of Hamilton's and our misery.