Realpolitik: American foreign policy under Washington, Adams, and Jefferson was aimed at threading the needle between England and France, avoiding European entanglements. Getting involved in Haiti would have angered at least one of them. Better to sit back and let the European empires expend their own resources.
Also, intervention would have been impractical militarily. Haitians had already defeated a 44,000 man army sent by France. France suffered as many combat deaths in Haiti as Americans did during the Revolution. The United States had a very small standing army at the time (7,000 at the start of the War of 1812), and most of it was tied up fighting American Indians on the frontier. As the War of 1812 would show, militia were ineffective when not fighting on their home territory. So the United States would have had to suffer great casualties in order for a cause that wasn't its own.
In short, Jefferson wanted an independent, white-ruled Haiti but did not have the military means to achieve regime change. Instead, he turned to economic coercion:
As president, Thomas Jefferson encouraged the independence of Saint
Domingue (as Haiti was then called) from France, but he refused to
recognize the new black regime and even embargoed trade with the
Obviously, the embargo did not work.