I looked up some dimensions online and found that there's and inner and outer turn radius limit for a U-turn. When the median is very thin, then the inner turn radius is too small, which makes the outer turn radius spill into the second lane. However, with an outer turn radius needing to be at least 24 feet, and our roadway lanes being 11' (sometimes 12' wide), that's why you'll see No U-turn signs at many four lane intersections. For example, McCormick at Monument has a No U-turn sign. And similar to that intersection, I've seen pickups not make the U-turn at Kernan and Kernan Forest. However, right now it's legal to try it on Kernan, and you don't always get an arrow to turn, like on McCormick.
The solution isn't as bad at Kernan Forest as it is at McCormick and Monument, since you could just have traffic enter the neighborhood traffic circle and circle back out, though it might make more sense to create a dedicated u-turn spot in the median between Kernan Forest and Goodwill.
You might be wondering what happens when there's an accident at an intersection where no sign exists yet isn't designed for a U-turn. Well, I've told my family to be very careful exiting the neighborhood, since u-turners with a green arrow or yellow flashing arrow still have the right of way, at least until city engineers finally put the intersection into compliance with code. But it's also a good reminder at every intersection to be aware of the illegal turns you WILL see in Jacksonville, since signs, traffic signals, laws, and basic common sense don't apply at most intersections.