Many people managed just fine on phones smaller than the 5S for several years. My hands haven't gotten any bigger.
Sure, the additional screen size provides for benefits - no question there.
But for some people that additional size isn't worth those benefits in terms of other conveniences, like fitting in pockets, purses, etc.
Perhaps the strong 5S sales are a result that a large part of the population prefers the smaller form factor.
There are people who do prefer the smaller phone. I'm not hating on them but for me and clearly a lot of others based on the numbers Apple and Samsung do, many love the bigger screen. I like the bigger screen for media consumption and I can also see the text on the phone without holding it super close to my face. The retina 1080p display on the + and especially the quad HD Super Amoled display on the S6 Edge...make for some excellent viewing angles. One thing I never understood tho, is the "it doesn't fit in my pants pocket" argument. Exactly what kinda pants are people wearing lol? My S6 Edge, which is pretty much the same size as the iPhone 6, fits in my pants pocket just fine. No issues at all. They're just regular pants.