I grew up going to WDW almost every summer (was sent to relatives in FL each summer). My aunt always rented a stroller, even when I was 10 (I was shrimpy, my 3 years younger cousin was bigger than me starting from when I was 7). There were no hand held games during those dark ages, so we still had fun pushing each other/getting a ride and looking at everything. There are tons of pictures of her and I after we stuffed ourselves into it at the same time (they just had these big one-person blue things back then) and had totally sacked out curled up around each other. The pictures are cute, and I'm sure it kept my aunt and uncle sane, and it turned neither my cousin nor myself into soulless uncreative lazy people.
My cousin has never been fat, so don't worry, your kids only have a 50 percent chance of catching the fats if you dare to rent them a stroller at WDW for your rare vacation. :P
When you do not ride in a stroller every day, it might seem like a novelty. I bet that is part of the reason why the OP's kid is asking. Just let her ride in it for a few minutes if she's asked for pete's sake. Probably she'll get bored (unless she's genuinely tired) and then you don't have to worry about it.
Who cares what other ignorant people might think if they bother to notice your child and correctly guess their age? You have a ton of people gasping over the internet because you're taking your family to a den of rampant consumerism and creative soul killing characters, too. Ignore them. Let your kid try it if she wants to. Nobody cares or notices what your kids are doing at WDW unless they're throwing a screaming tantrum, throwing up over the side of the boat during the Viking boat ride, or peeing in the fountain (saw that in the line at Small World the last time we were at WDL actually!) and even then it's only momentary because they'll be in good company.
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