We took a stroller for ds who just turned 5 last April. He definitely didn't have the stamina for all that walking, and pushing him in a stroller was
so much easier on my back than carrying him, which he would have preferred over walking if he didn't have a stroller to ride in.

He was "only" 40lbs back then, which isn't a lot for a 5yr old, but it is a lot to try and lug around the parks, lol. We are going back in December, and will be taking the stroller again. I don't foresee us pushing him absolutely
everywhere in it. We will probably be parking it in stroller parking and making our way around the different parts of the park on foot, then retrieving it before heading to the next area, or out of the park. There is no rule that says you have to use it
all the time, but it sure is nice to have if your child is getting worn out, and it can make the difference between a happy child, and a cranky one. It is vacation, after all, where you're supposed to be having fun. We don't use the stroller at home any more. jmho.
eta: also, during really crowded times, putting a kid in a stroller is an easy way to keep them "contained" and close to you, and it's much easier to keep them from being trampled by some other guests as you try and make your way through throngs of people.
hth