I cant imgine NOT having a stroller. For those storage reasons for one. I throw my backpack on the handles of the stroller and away we go.
Our dc are 4 and 5. Old enough to walk, but still at the age where if we want to get from one end to the other quickly, put them and in go. DS is more of a walker than dd. She is Miss Princess. So we need the stroller for her for sure. If they get hot or tired, they can just hop in there.
We also fly, thank goodness they are not considered a checked piece of lugguage.
Lastly, I don't think there really is a solution unless carrying your things. As pp said, you could get anything bought sent back to your room. As for things you carry, is it better for you guys to carry them in backpacks or bags, or bring along a stroller? Which is best for you?
It will be nice to do a stroller free vacation, but at the same time if you have a lightweight easy folding stroller, shouldn't be too much of an issue. DH takes one stroller, I take the other, we are pros at folding them up quickly by the time we are done in Disney.
If you are going in warmer months, the worst is to have to carry a backpack and getting very hot with it on.
Last thing, our plan is to park our strollers somewhere around the carousel in MK. From there we will walk around the park, train is available to get around in, and our strollers are central. We don't need to bring it EVERYWHERE. But in Epcot, they will be nice to have, same for HS and AK. But it is an option to park it for half the day if you are comfortable with leaving your things.