Your statement "A 7mm08 with the proper bullet will kill anything any of the cartridges you named will.", is ludicrous.
As for my "buddies" who flinch, I was speaking of the customers who used to come into my gun store and tell me their tales of woe about the huge elk/bear/Alberta Whitetail/etc.
they "hit really good" but couldn't find. Fortunately after years of birdhunting and bowhunting, the guys who taught me about rifles and rifle shooting had real knowledge and liked animals to be
dead where they stood.
Your customers are EXACTLY the ones I was referring to.
If they "couldn't find" they don't KNOW where (or even if) they hit it.
They won't admit to othemselves
they made a poor shot, so they go with a larger gun to make up for it, and the problem gets worse.
"Dead where they stood" is not a
realistic expectation with ANY cartridge unless you hit the CNS.
Also the OP stated she liked the 243 because
she could handle the recoil, so it's not likely she would shoot a much larger cartridge enough to become proficient.
The 7mm-08, is accurate, a joy to shoot and is great for lots of stuff, but to say it will dispatch anything that a 7mm Mag, (no favorite of mine), or the 300 Win, is just not right. The kinetic energies listed on ballistic charts tell the story. Speed doesn't kill, but kinetic energy/shot placement and good bullets do.
An animal won't notice a few hundred ft lbs difference at reasonable ranges.
John Taylor killed most every kind of animal in Africa with a 7 MM Mauser.
Jack O'Conner took most all the North American animals with a 270 Winchester
That's before everyone "knew" you couldn't kill them unless your cartidge said "Magnum"