I disagree somewhat... yes, cooking matters BUT very fresh eggs are always harder to peel.
https://www.seriouseats.com/2009/10/why-fresh-eggs-are-harder-to-peel-food-science.html
Ever since I started making HB eggs in my Instant Pot, I've had no problems peeling them. And only a few had any green/gray on the yolks. I was skeptical, at first, but it works!