Our first trip to WDW was back in '99 when my dd was 5, turned 6 at Disney! She hadn't been in a stroller for years. She was, still is, very tall. Would I have considered using a stroller? Maybe.
Here's my take on the subject. Yes, WDW is a huge place, and it sure is tiring to get around. BUT....I find that if you take a stroller, and let the kids ride in it, you tend to rush from thing to thing. You spend more time running around because you can....the kids don't get tired. If you choose not to use a stroller, you tend to take more time as you move about the parks. You notice more. Yes, the kids get tired...heck, I get tired! So, sit down, relax, watch life go by for a bit. Do an attraction that allows you to sit for a bit. Go eat...whatever. If you take things at your kids' pace, yes, it will take you longer to do things. But...by the time you get back to the resort, at the end of the day? Your kids are pooped and more than ready for bed!!! A nice plus.
But, if you choose to use a stroller, then stop worrying about what others may think. No one knows your situation. I know that I have looked askance at a family with kids in a stroller. Why? Both the kids had to be careful not to drag their feet on the ground and trip up the parents while riding. They were very tall for a stroller, and probably well past the age of 8 or 9. But was it my business? Nope. If mom and dad want to push kids that big in a stroller, have at it!!! Their choice. Most people aren't going to care one way or the other.