Bloodletting is actually still used to treat some diseases - for example it is the primary way to treat Haemochromatosis.
Until recently, in the UK at least, people with this condition couldn't donate blood, so it was just thrown away like back then too - though more recently they started allowing donations to help treat hospitalised anaemia.
Wish I could donate blood, but alas, I'm on some prescriptions that would make the recipient unhappy, and I'm not about to try not-professionally-conducted bloodletting.