Here's a non-horror story. I flew into LAX 2 weeks ago. This was my 2nd time to fly into LAX, both times were chosen for the nonstop flight option.
This time it was just me with my 6 year old daughter, 16 year old son and his friend. Getting to baggage claim took a little longer than I was used to, but that was no big deal. (My preferred airport is Long Beach.) There weren't tons of people heading to baggage claim or waiting around. It was very calm and quiet for us. Zero crowds. I had
arranged for a shuttle pick up with MidWilShuttle ahead of time. I was directed to text them when I arrived and let them know what "column number" I was standing next to on the little island outside, across from baggage claim. There were no other people standing near us -- closest was at least 30 feet away. Shuttle arrived 5 minutes later and we were off. Pulled away from the curb at 2:14pm and arrived at our hotel on Harbor Blvd at 3:07pm.
I have no experience flying out of LAX, and at this point I wouldn't choose to do so. Both times I flew into LAX were good experiences, with no issues whatsoever, and I wouldn't hesitate to fly in again.