This is a conflation of numerous things, and kind of a denial of physics.
Energy retention is a matter of density. Lead holds energy better. At any given range, lead will have more kinetic energy retained.
Use steel if you have to, or want to, but be aware of this.
If you hit the heart/lung area it doesn't matter. No real meat loss.
But you certainly don't need that kind of power. I shoot rabbits on my property with a .25 FX Wildcat airgun. It puts out about 50 FPE at the muzzle. Rabbits hit in the chest out to 60Y go nowhere - usually one kick/flop and...
Cottontail populations here in WI are cyclical, as others have said. Some years I can shoot 8-10 on our 3.5 acre property without trying (just looking out the windows occasionally), other years you see one or two all year.
If you want motivation, they kill pets like mad wherever they're common. Farm birds too.
We have chickens. I've yet to shoot a yote but I did kill a fox that took our rooster several years ago.
It's hard to imagine how a less dense material could perform better, ballistically, all things considered.
There's no way that losing energy faster is ever a plus.
I say go heavier than lead - #9 Tungsten is devastating on turkey!