Continuous downspout? It's unwise — and ugly

Q: I have gutters and downspouts from the upper roof of my two-story home that drop water down onto a lower roof. The lower roof drains this water down into the gutter below. It seems like this increased water flow on the lower roof would cause much more wear there. Why don't the downspout pipes continue from one gutter to the next?
A: Downspout lines are not extended across the roof simply because they are not attractive. When you have a long run from one gutter to the next, a large pipe running down the roof is a hideous sight. Furthermore, a pipe on the roof is subject to damage from people stepping on it or tree limbs falling on it, and it is more prone to plugging (as is the gutter).
More importantly, a downspout running down the roof would have to be secured to the roof. That would mean putting nail or screw holes into the roofing. Every hole is a potential leak point.
There are ways to attach this pipe without holes through the roof, but the cost is prohibitive. Thus, another reason you will not see continuous downspouts.
All that said, you raise an important issue about roof wear.
Roofing materials, particularly in composition roofs, are subject to greater wear beneath drains. Sometimes that extra wear requires replacement of a small roof section before the remaining roof fails.
Leaks inside walls are more likely if step-flashing isn't installed correctly — where upper walls meet lower roofs on a pitch. Ever see water screaming out of a second-floor downspout, onto the lower roof and right off the edge laterally? This happens a lot because the roof overhang always has a slight outward tilt.
Do I have a better solution? Nope. Like everything else, it is a trade-off and ultimately a function of the design of the building.