I don’t entirely disagree with you, but I’ve boiled eggs. I’ve peeled boiled eggs. I’ve never once given boiled eggs and ice bath - I didn’t even know that was a thing until I saw a roommate doing it in my early thirties (though to be fair I didn’t have my first boiled egg until my mid twenties).

I’ve definitely peeled eggs poorly, as shown in the OP, but I’ve also peeled them nearly perfectly with no ice bath. I don’t know if it helps, but it’s not necessary.