I can certainly see the point of hunting beaver without bothering too much with retrieval.
Quite often they are pests, building dams and destroying valuable forest or property, digging holes, plugging drain lines etc..
I was beaver hunting here last spring. Since i was after the fur and meat, and the water was 0°C, i ended up just watching swimming beavers at close range through a riflescope, never taking a shot.
However, the landowner quickly determined that my progress was too slow, and brought in the cavalry.
He used a total of 12kg dynamite to blow up 4 beaver huts, complete with beavers and all.
Talk about not retrieving them...
K