Dd, now 17, was out of a stroller at age 3. If she needed more time to get from point A to point B, we took the addtl time. If she got tired, then we stopped.
When she went to WDW, for the first time, she was 5. We took things a bit more slowly than we do now. She seldom got overtired from walking. Here's my rationale....when a child is up and walking, they get physically tired, which is pretty easy to do. You stop, relax for a bit, smell the roses so to speak. Maybe you grab a bite to eat, maybe you head back to the resort for a few hours. But, if your child is in a stroller, they are still being over stimulated..there is no way around it. WDW is an incredibly stimulating place. And the vast majority of kids can't take hours on end of that type of stimulation. So...if they're relaxing in a stroller, they aren't physically pooped out but emotionally/mentally, they are being 'assualted' by the sights and sounds of WDW. And this gets to a child after a bit. They start to get cranky and melt down..but the poor parents figure the child is just tired so keep going..after all, junior is being pushed around, how bad can it be???I prefer to go with the physical tiredness vs mental tiredness. It's so much easier to deal with. So, I let my dd walk around and get tired. We then would get a drink or bite to eat and get away from all the stimulation and she would bounce back pretty quickly.
But, that's just me. It worked for me, may not be what others would choose to do. We don't do commando type touring...we are more laid back and not in any hurry. If we need to take a break for a few hours, so be it.