I was watching the startup sequence for an A320 and it struck me as unnecessary minutiae to ensure the wipers are off before power on. Is there something important that I'm missing that puts windshield wipers in the same list as thrust and gear levers?
For the same reason you should turn your wipers off when you shut off your car (since very few people go through a power-up checklist in their car...):
Running the wipers on a dry windshield can damage both the wiper and the windshield as the dry blades drag small particles of dirt, grit, rocks, etc across the windshield. These particles can tear up the rubber of the wiper, and they can scratch the windshield. Dragging dirt and rock particles across a wet windshield isn't inherently good for either wiper or screen, but the water acts as a lubricant and significantly reduces the damage potential.
It's far cheaper to print an extra line in the check list and have the pilots take 5 seconds to check it than it is to replace wiper blades and windscreens.