You could say that actually bloodletting was practiced by a Founding Father, and enthusiastically practiced at that. Dr Benjamin Rush was a signer of the Declaration of Independence and a Pennsylvania delegate to the Continental Congress. He was a firm believer in Heroic Medicine, which ( as the name implies) required bloodletting. Although the practice went back quite far ( was tied up with the very old idea of humors in the body needing to be balanced) in Rush's case he thought that the flushed appearance of a fever patient indicated an over-stimulated circulatory system, and that bleeding was the best remedy to correct that over-stimulation. Heroic Medicine was common in the later 1700's, and ingenious mechanical devices were made that could quickly slice or poke holes into the patient's arm or leg.

Rush's interactions with Washington were not completely friendly. He was only one of two Delegates who voiced the opinion that Washington should be superseded in the Continental Army , in the very hard year of 1777. Though dogmatic when it came to bloodletting, he had much more advanced ideas about the care of the mentally ill. He was also counted one of the more lively minds in Philadelphia, advocating for abolition of slavery and education for women.

Heroic Medicine seems to have faded after around 1850, when it was noticed that taking care of patients with infections produced better results than draining their blood. But as for the death of Washington in particular, it seems pretty clear that his infection had become quite extreme, by the time the doctors drained more than two liters, and that only a tracheotomy to keep him breathing would have given him any chance of survival. In other words, bloodletting might have killed him, if suffocation hadn't killed him first.