My automatic Rubicon likes to be stopped and in neutral to go to 4lo, my manual likes to be moving a tad usually.
I'm with
@jjvw on shifting out of 4wd at speed... unnoticeable.
On the comment 4lo for not getting stuck vs getting unstuck...to me it's terrain specific. In the east , 4 lo may get you stuck in mud 4hi will carry you through, and 4 high may make you break traction where 4 lo helps you hook up. Shift on the fly alone can be handy for a number of reasons.
I used to think 4 wheel drive of any kind was the answer to most of life's problems...'til I discovered lockers. Holy moly.
It's great you are getting out and playing with it, and learning the nuances...keep doing that 'til it's second nature. When you need it, you want it to be an extension of your mind. Shift on the fly is a great TJ feature and can give you fast traction at speed that can carry you through junk. It really can be important to know when you can shift it in or out most all the time....over time that becomes instinct.
Sometimes stopping one, going to reverse, then back to neutral seems to take pressure off the driveline or sync things up.
Good thread, good questions and good on you for learning your equipment.
Reference note-
Jerry mentioned not synchronized. That's actually a Jewish thing, and we don't want to get too deep into religion and politics.