I've never seen anyone wear a skort, and I wouldn't dream of wearing one. I wonder if it's an age thing -- I'm old enough to remember when women/girls weren't "supposed" to wear pants in many situations. So to me a skort would be symbolic of an oppressive era.

I looked at some cycling skirts online, and I can't figure out how they differ from a regular skirt over bike shorts.

Most of the bike shops I visit are small, and I wouldn't expect them to offer much in the way of clothing. It just wouldn't be practical for them to maintain the inventory.