The correct way to hardboil eggs is actually to steam them, which is what the majority of the world does (have you ever seen someone selling hardboiled eggs? They are usually in a steam container). If you time it right, you don’t even need the ice bath to achieve an easy peel egg (though this takes practice lol).

Boiling is just a alternative method that is slightly less effective but very common because not everyone keeps a steamer basket at home.