I personally never had an issue with "crossing the park" to get anything, whether it was an FP or a pretzel, pushing a stroller or not, family in tow or alone. Never even really thought about it, didn't find the parks that big and walking even at a brisk pace has never been anything that bothered me, inside or out of a theme park. I guess I should count myself as being fortunate to be in decent shape. It's only when I'm standing in a line that my feet start hurting. Really hurting.
But the days of paper FP's are numbered anyway, by next week they will all be gone, history, a thing of the past and we can focus on the strengths and weaknesses of the new system and how best to use it to it's full advantage.
Provided, of course, tiers and park hopping and duplicate attraction and limit three are all addressed.