The .243win is a lot of sauce for coyotes, such it can do a lot of damage to pelts. For 400-600, or longer shooting, the 22cal centerfires aren’t as reliable, so the 243win and the like start being more advantageous. For depredation prevention, not concerned with hide damage, it’s hard to complain about the 243win.
My first coyote rifle of my own as a kid was a 22-250, but my second was a fast twist 243win. At the time, I was happy to spend time sewing holes in coyotes, and worried more about recovery and protecting calves than minimizing pelt damage. Since then, I have come to find the 223 rem to be the ideal coyote rifle, but would seldom recommend against the .243win.
The 87 Berger VLD Hunting bullet over Varget or H4350 is a very good starting point for a 1:9.25 to 1:10” 243win. Not fur friendly, but it’ll sack coyotes as far as you can hit them.