For me taking a break has nothing to do with the age (and definitely isn't limited just to children).
Four out of the five people in my family are introverts. Contrary to what most people think that doesn't mean you're shy. It just means that you need some quiet time alone to "recharge your batteries". Our home is a quiet and calm place to escape after feeling "drained" by too much socialization (school/work/etc).
While we absolutely love Disney, the crowds are simply way to much stimulation. It's extremely loud, hot, and claustrophobic having people surrounding you constantly. If we did not take a break, we would all be completely miserable by the late afternoon. We like to go at rope drop (usually EMH), get as much done as possible, and be headed out by the time the crowds are pouring in (around 11). I know to many a midday break seems like a waste of time, but for us it's some of our most valuable time. Even just an empty bus or monorail ride in silence can be so relaxing.
Rope drop to close actually sounds like a miserable, anxiety filled, meltdown-provoking nightmare to me. Sure, we would have more (quantity) hours in the parks, but the breaks allow our family to have more quality hours in the parks.