The problem with labeling a caliber choice "unethical" is where is the cutoff point?
If the 22 centerfire is all one can shoot due to injury or aversion to recoil, what are they supposed to do? Not hunt?
Shot placement trumps all, when it comes to quick kills on game.
WDM Bell, an ivory hunter from the early part of the 20th century killed most of his over 1,000 elephants with the 275 rigby. That nearly obsolete cartridge is comparable to the 7x57 mauser cartridge.
He was a very good shot.