Fun fact! Apparently one of the bigger obstacles in clinical leech application is their tendency to migrate (I've learned this anecdotally from online discussions in nurse communities). This is a pretty big downside given that modern leech therapy is generally done to ensure adequate bloodflow during and after things like microsurgeries where the therapeutic area is relatively small.
Apparently the trick to it is to take the plunger out of a disposable syringe and stuff the leech tail-first down into it. You can then use the little wings on the top of the body of the syringe (where you would normally brace your forefingers when using a syringe to inject medication) to anchor the tube against the skin. This makes a tight little plastic capsule to keep the leech feeding on the correct area for the length of the therapy (not much longer than a few hours if I understand correctly) and that will contain them neatly once they've detached themselves and are awaiting disposal.
Imagine if your whole life was being born into a sterile void, being laid in front of a bacchanalian feast to have your fill, then promptly executed. I can't decide if I'd be down for that or not. I can definitely identify some upsides.