https://www.seriouseats.com/the-secrets-to-peeling-hard-boil...
I've inadvertently run this experiment many times. For years I followed Alton's original Good Eats instruction and started with cold water. Shells were always hard to peel. After Kenji's article I switched to adding eggs to boiling water, and it makes a huge difference in peelability. Also, cook time is more precise because the water temperature is constant; different ranges/burners/pots/waterlevels boil at different rates.
The only problem with starting in boiling water is that if your eggs come directly from the fridge (ie store bought eggs) some will often crack from the heat shock. This can be mitigated by putting eggs in lukewarm water for a few minutes first. Or just get chickens and keep your eggs at room temperature :-)