Yes, the stroller topic is always a heated one, mainly because it's an issue between what's good for the kids, what's easier for the parents, and the obesity epidemic in the United States.
My family is fortunate to be active and healthy. My kids have always been active in sports, we only used a stroller for one trip to WDW, when youngest DD was 2. My older DD was 5 then, and did fine, in May, for four days of walking around WDW. Next trip, no stroller for the then 5 and 8 yr olds. Again, they were fine, for 7 days. But they have always either been dancing, skating, playing soccer, or doing gymnastics. We also hike up mountains in the summer.
But not all families are this active, and some kids are more whiney than others, and some parents want to hurry around WDW and not rest as much as their kids need to rest. If those parents want to push their kids around in strollers at WDW, good, at least the parents are getting some exercise. I don't think they are doing their kids any favors, as it enforces a mentality that I don't agree with, but I do see how it makes their vacation easier. I don't think it makes the kid's life any better, and it saddens me how out of shape so many kids are. How can it be that the parents can walk so much, (and even push 50-80 lbs of kid and carriage around), but the child can't? Why are the parents is such great shape, but the kids aren't? My then 8 yr old could have walked/run circles around me the 7th day of our trip!
That's the only reason I feel that the OP should just bring a single stroller for the younger child, and see if/when the older one gets to the point of needing the stroller and then renting one. What kind of message are we sending our kids if we let them sit on their butts so much? Why not try to see how much walking the kids can do? Why assume that they can't?