Not OP, but apparently they're useful for when you want a continuous, slow drain of blood. The ones they breed for hospitals don't carry disease, so you can just kinda plonk it onto the spot that you want blood out of, and replace it when it gets full

Wait until you find out what they still use maggots for...

It's less about the blood they suck out and more about their saliva. It's a natural anticoagulant.

Amputation sites I think? The suction attracts blood flow to the area and supports healing/retention of blood vessels... I think. Neither one of us clearly can be bothered googling but that's what I recall...

For skin grafts after burns; the leeches' saliva has anticoagulants that helps blood flow through the microvasculature (tiny blood vessels) of the area. This helps promote growth of new blood vessels, as well as improve the health of the current blood vessels in the area.

TLDR: Helps tiny blood vessels in skin grafts (and other procedures), reduces failure of said skin grafts

Others have already mentioned limb reattachment and anticoagulants, but if you're interested in learning more, I highly recommend a book called Dark Banquet: Blood and the Curious Lives of Blood-Feeding Creatures. Leeches, mosquitoes, bedbugs, and vampire bats are fascinating!