"Why is the default position seat-down?"

Simple, as another poster said, men also use the seat down at times. So mathematically, the seat is used more often in the down position. Or do you shit standing up?

It doesn't only 'matter at the moment of use'. It's also way more hygenic to close the toilet when you flush, and I'm assuming you flush just about every time you use it. Numerous studies show that germs cover the entire room with each flush if it's left open. I doubt many people want to close the cover and seat, flush, then raise the whole thing up again.