We used to have egg hunts in our backyard with the pretty hard boiled eggs. The fear was always missing one and having it rot! One person would hide all the eggs and then the others would look and whoever got the most eggs would get to hide them next time. That was the real treat - it was often difficult to find good hiding spots when the grass wasn’t even growing yet. Everyone would end up with a turn hiding them but things did get competitive between the kids and especially with H. The kids were older then so they enjoyed trying to outrace Daddy to grab the egg on the tree branch or fence.
Littler kids need to be protected though, and just allowed to have the joy of finding things without worrying who got their first or how many someone else has.