Around THIS Campfire, elk aren't tenacious or tough.
In the actual elk camps and around actual campfires talking to crusty old pharts who've been hunting and killing them a long time, I hear otherwise. And I know two very close to first-hand tales of elk tenacity.
Some critters are reputed to give up rather... resignedly. Caribou and moose come to mind. Elk appear (to me) to have a tendancy to really go the other way, and at least sometimes do some pretty superhuman <grin> things when hit pretty hard.
My two elk were both well-hit and went down quickly. Then again I had a whole millimeter on the wimpy 7mm guys!
I'll buy that about anything will kill an elk, but I won't buy that they are not, sometimes, a notably tenacious animal. And elk habitat being what it is, at least IME, a quarter-mile death dash can be veddy veddy bad.
So- hit 'em right, that's key. Hit 'em hard also seems desirable to me.
.338 Win Mag is the best Elk Cartridge in the World!