If you bring the water to boil before adding the egg it is much easier to remove the shell
Edit: I see my comment doesn’t really relate to your comment. I’m tired
That’s a myth and unrelated. But throwing it into the cold water helps preventing the egg from cracking.
But timing it is surely much easier when the water is boiling. If you just slam it in cold water then you are at the mercy of whatever stove you are using
I just poke a tiny hole in the bottom. And keeping them at room temperature also helps a little, if I’m too lazy to poke.
In my own experience boiling hundreds of eggs over the last couple of years I found that if I don’t start with boiling water then the shells are very difficult to get off. If I start with boiling water the shells slide right off.
From what I can tell it depends on the eggs themselves, maybe their freshness, but it is almost always a certain batch of them that have this issue. Doesn’t really matter how you boil them, or if you put them under cold water afterwards. They’d be hard or easy to peal regardless.