Your local hospital quite likely currently has a tank of leeches. They are still used in surgery. Especially after reattachment surgeries. They secrete anticoagulants which prevent blood clotting. They are also used in microsurgery to increase blood flow to a certain area.

Is there some reason why we can’t either extract those anticoagulants from the leeches or otherwise synthesize them?

From Wikipedia (https://en.wikipedia.org/wiki/Hirudo_medicinalis)

> Because of the minuscule amounts of hirudin present in leeches, it is impractical to harvest the substance for widespread medical use. Hirudin (and related substances) are synthesized using recombinant techniques. Devices called "mechanical leeches" that dispense heparin and perform the same function as medicinal leeches have been developed, but they are not yet commercially available.