I supercharge almost every week (I travel a lot for work). Some notes.
The best way to absolutely kill your charging rate is to leave your car out in the cold for a long period of time and then supercharge. I've done this numerous times, not really on purpose, but just out of circumstance, and a typical charging cycle is to start low, at about 20 - 40 kW, which increases up to about 60 to 70 kW max, then tapers back off near full back down to maybe 20 kW. This makes for a terrible charging experience. If you have to stay unplugged over a cold night, try to arrange to supercharge that evening rather than the next day.
On a good day with a low battery, I get up to about 110 kW when first plugging in, and that tapers pretty consistently over the charge down to maybe 20 kW near full. At roughly half charge, I'd say the typical charge rate is about 60 kW. Not great, but okay. I would like to see this improve in the future.
If you have a nav destination set, the car provides a nice feature of telling you how long you need to charge until you can continue the trip, and even sends alerts to the phone. This is nice, but I find the estimated time to be overly optimistic. However long it says you will need to charge, it will probably be longer.
I once ran into a charger that was only giving me about 50 kW even though battery charge was low, no other car was there, and the weather conditions were not a factor. I switched bays and started getting 90 kW. Not sure what the deal is, but apparently it's possible for a supercharger to under perform without being totally broke. This happened at a stall at the St. Louis/St. Charles, MO, supercharger maybe 6 months ago.
I once had supercharging fail shortly after starting. I unplugged, plugged into the same stall again, and then it worked fine the rest of the time I was there. So good to keep an eye on it just in case this should happen to you. Would suck to go somewhere for half an hour, get back, and find the car had stopped charging after the first 5 minutes.
I'm not convinced that the first person to start charging at a shared pair really gets priority. I have an anecdotal personal experience that brought this into question. I once proposed getting together with another Tesla owner for a day to run paired charging tests with our cars, but so far no one in my area has been willing to be that much of a geek, so I haven't had the opportunity to do thorough tests to prove it one way or the other.
Overall, supercharging makes long distance travel a reality, but it still needs to improve further in the future if EVs are to take over as the primary form of personal transportation. If it could manage 90 kW average for the entire charge required for the next leg of a trip, that would probably be sufficient. Whether that be accomplished by a higher max charge, bigger batteries allowing lower percentage charges and thus less taper, or improved battery chemistry that reduces required taper, any one or combination of those solutions would suffice.