As for the pay-to-play, I think it's more than just maintenance that elevates them. Private courses have more freedom of design, and often better property to start with. Plus, they can be less crowded, and have less overlap with non-disc-golfers than you encounter on public property.
Absolutely. Also, many of them have significant amenities that aren't within the realm of public parks' missions. I've visited courses with pro shops, warm-up areas, clubhouses, driving ranges, a three-story gazebo, restaurants, food trucks, a swimming pool, paintball, cabins for rent, fishing poles for rent with a stocked pond... It can be tough to decide how to factor in those amenities when rating a course, but those things certainly add something positive to the experience.