I airdry, and it takes my hair 8± hours to completely dry. But I only wash my hair once a week. It takes considerably less time to dry with no product, but that's a moot point.
The other days I spritz it with water or Awe Inspiraling and maybe use other product lightly. Whatever I put in, it just soaks it up! I do spend the last 2-3 days before washing again with an up-do, usually.
As for going out with wet hair, it does happen sometimes. I'm someone who walks and bikes a lot and it seems to dry quicker en route, because of the wind or something. I know that the minor inconvenience of wet hair in public is better than drying out my hair with a hair dryer.
Now that I've moved to a colder climate, I may have to use a hair dryer occasionally because it's better to do that than have wet hair freeze and break. It's really too bad that these things go hand-in-hand: 1) using a dryer to avoid wet hair freezing and 2) winter heating. My poor hair doesn't know what's coming.