Sometimes institutions mutate greatly over time, obscuring what they were originally. Medicine for instance is a true science today, or at least it tries to be one most of the time. Throughout most of human history, it was not. While basic nursing care, give the person food and water and a clean environment, was effective, you can’t credit doctors for it, since any peasant would have told you the same thing. How valuable was the advice they gave specifically? I would guess much worse than no advice, though I haven’t been able to find any objective studies. Could you really blame them? I would argue that if you can blame pre-modern religionists and witch doctors for their unscientific notions, for believing in the effectiveness of the rain dance or the spiritual potion or the prayer, you should also point the same accusing finger at the bloodletters. Likewise, if you admire pre-modern religious skeptics, you should also admire pre-modern medical skeptics.
It reminds me of an old joke which goes something like “the Tsar learned that the Russian provinces with the highest death rates from the plague had the most doctors, so he ordered all the doctors to be shot.” This is supposed to be making fun of Russians, but if you consider the stats gathered by Semmelweis, you realize that maybe shooting the doctors would have been an effective humanitarian measure after all, at least from a consequentialist standpoint.