I've tried to post this a few times, but I think my post is too long, so I'll cut it into sections.
I just completed a somewhat decent road trip where I had to preplan the route for using superchargers. I'd be curious to get other's feedback and experiences. Here are my observations.
The first thing I would note is that when you plug your car into the supercharger, do not immediately walk away from your car and grab a bite to eat. Stay with the car for about 5 minutes to ensure that the charge is working and that the kW remains sufficient to charge in the time you've anticipated.
Here is what happened to me.
At one charger I stopped at, I plugged in my car, it started charging fine so I walked about a block away to get some food. Right as I arrived at the restaurant, my phone alerted me that charging had stopped. I was not able to restart it from my phone so I had to walk back to the car. It appears that the supercharger had over heated and would no longer work. I had to move my car to a different charger and plug it in. It worked fine second time around.
Another spot I stopped at, I plugged in and it started charging just fine just north of 100kW (which was providing about 400 miles each hour of charge). It told me I had about a 10 minute wait (which matched what I'd preplanned using the Tesla trip planner). However, about five minutes into the charge the kW dropped significantly to around 40kW and my car's display now said I had 40 minutes to wait. I unplugged the charger and plugged it back in and the same thing happened almost immediately. I decided to move to a different charger and that one delivered max capacity kW just North of 100kW again and completed the charging the car to the level I needed in 5 minutes.
It was extremely hot both days this occurred (over 100 degrees out), so I suspect that had a lot to do with it.