I went last Tuesday and never got over 72kW, even with a warm battery under 50% SoC.
I'm not a huge Supercharger user, but I consider myself pretty "lucky" when it comes to getting great charge rates out of Superchargers, especially compared to what I've seen posted on Plugshare and here on the fora. But yesterday was one of my rare long trips and I noted several interesting observations. In all instances I was not sharing a charger with anyone, and my battery was properly conditioned upon arrival (I'm not sure it explicitly had to condition the battery nor not).
At one stop, my charge rate appeared to start out at a reasonably high rate (over 120kW) so I went into the store and when I came back out, the charge rate was pegged at 72kW. I switched to a different stall and the rate came back to 120kW+.
Then at another stop I again had an initially high charge rate, but then it again seemed to plateau at a lower charge rate that I had expected (versus a taper). Here is a charge of that second charge:
This is not a typical taper-off behavior with the plateau in the middle.
I also observed that the charge rates of the plateaus were suspiciously even--and familiar--numbers like the 72kW you mentioned (even though the plot above shows 99kW, I seem to recall the number in my car was around 96-97kW.
I'm sure someone will correct me if I'm wrong (or point to a more authoritative source), but I know that the components inside Superchargers are actually the same (or at least similar) onboard charging units found in the vehicles themselves, each one with a capacity of about 12kW(ish), which means we see a lot of multiples of 12 in charge rates (72kW, 96kW, 144kW). It would appear to me that when your car is stuck at 72kW, that basically means that only 1/2 of the units are functioning. This may be be expected, in the event that you are sharing a V2 charger with another stall, or your car/battery is not capable of utilizing more than 72kW (cold battery, or high SOC), but it's also simply possible that the charging units have failed, although in my observation, the fail was not hard in that it had been initially working and then failed. So maybe it just overheated or something. Either way, I imagine the fail should be detectable by Tesla. It's frustrating that Superchargers seem to sit for days/weeks with crippled chargers, and there is no easy way to tell that a given stall is failing in this way.
With a V3 site such as Bethel, the architecture is slightly different, but it's basically the same idea. If some of the chargers in the cabinet are down, the behavior appears to be a steady, but reduced, charge rate.