I use a .308 on our little Idaho elk..
^^ This ^^
Is it because you can't handle recoil?
I know you were commenting tongue in cheek, but there is a glimmer of truth in it.
I have noted that I can shoot substantially better with cartridges that are not hard kickers. I would rather be able to shoot a 3/4" group with a .308, than a 1.5" group with a .338.
I find that I can place .308 win rounds with precision, with little fuss.
In fact I popped a cow elk a couple years ago in the noggin, at an extended range. The herd was standing bunched up, milling around. There were no clear shots that did not run a risk of shooting through and hitting another elk.
Finally one cow stuck her head out away from the group and I put one in her ear. I was proned out, had lasered the elk repeatedly and was shooting my Sako TRG, which is a true sub 1/2 moa rifle.
400 yards and closer are chip shots with that gun. It pretty well shoots itself.
To be clear, I am NOT an advocate of head shots. This was a unique set of circumstances, and I had a heavy target rifle, which made the shot a high probability one.