Are Cougars supposed to respawn?

So I went hunting for the Sundered Pass Cougar. I lit a fire and eventually killed it. Yay, pelt and claw! All good, right? No, because two other cougars spawned in the region. I thought that mechanic was supposed to mirror the cougar expanding its hunting ground and coming toward you, but instead its two more separate cougars. One spotted me on the way back, so now I have two pelts and two claws. And I heard the third roaring somewhere else. But heres the kicker:

I went back to the second cougars territory, which I had killed and so assumed was safe, but there was another cougar there!

This is ridiculous. I like the cougar as an idea but its way over-pushed on the player. I get the “its spreading out its territory to find you” but I thought killing The Cougar would wipe it from the region. There are now the traces of four individual cougars in my map within the span of three days.