As others have said, it's all about you, your child, and your touring style.
In my case, DD was a rather scrawny 7-turning-8yo at our first visit (she was the weight of an average 4 year old, and the height of an average 6 year old). She would have adored a stroller, as would I. We didn't bring one because of her age (and seriously, we hadn't had a stroller in years, so we would have had to figure out who to borrow one from!). By the end of a full day, she was ready to be carried, and I was cursing every single step to get to our hotel (Super 8 at Harbor and Katella).
We're definitely open-to-close, go-go-go-go tourists and we average 12 miles of walking a day (high of 14 miles!). That's a lot of walking for 2 obese adults and 1 preteen... For the average 5yo, that's a heck of a long walk, both in mileage and pure hours of walking!