I stopped by the Williams SC on Sunday evening and only got a max of 128kW, even though my battery was warm (I navigated to the SC and it showed preconditioning in the last 25 miles of my drive to it) and it was relatively cool ambient temps (in the 50's ºF), so it's not like the chargers were overheating.
So my battery could have theoretically taken much more power. In similar conditions, I was able to hit 240kW at Red Bluff two days earlier. I also noticed the power dropped by 5-8 kW when I turned on the heater while charging at Williams, which indicates some of the available power from the SC was redirected from charging the battery to heating the cabin.
I'm not sure if this SC was designed to be 250kW (thin liquid-cooled cables indicate it is) but is currently being limited to about half the power due to other issues such as power supply. Note I was the only car in the entire SC. As others mentioned, Tesla's website currently indicates 150kW max, despite in-car nav showing 250kW.
EDIT: I started the charge at 2% SoC and ended at 62%, so the limited power was definitely not due to my battery being "too full"