Haha, well, we brought strollers for our first trip (ages 4), and then we rented Disney strollers (two doubles) for our age 5 and 6 trips. So by that point they were only being pushed around in the parks (which despite no longer using strollers at home, did make our trips easier end enjoyable).
Our last two trips were stroller free because they were just too big at that point and it would have been silly. But everything is easier when you don't have to lug around multiple strollers. The only downside is now I carry around a giant backpack (refillable water bottles, snacks, ponchos, sweatshirts for the girls because they're always freezing in restaurants), instead of being able to just hang and leave all that stuff on a stroller. That certainly makes me a lot sweatier!
Oddly enough our kids never slept in their strollers when we were in the parks, even on long days. I guess we were lucky and they were pretty engaged and energetic. We also tend to do TS ADRs for lunch and dinner in the parks, so we get some good air conditioned breaks that let everyone rest up.
Even going back to the room mid-day when they were younger felt like a waste because they didn't want to nap, and when they did, they woke up in horrible cranky moods - worse than if we had just stayed out in the parks all day. In '16 and '17, we wound up doing all day park days in all the parks, and that required miles and miles of walking. I'm not sure if it's because we live in a city and do a lot of walking at home, but the transition out of using strollers was much easier than I thought. That first year of no strollers I really planned cut back touring plans, so we wound up just improvising a lot because the kids wanted to keep going.
We took this year off, but I'm really interested to see if they enjoy it as much next year as middle schoolers as they did as young kids. One daughter still even insists that she wants to go to CRT, but we'll see next year...