No degradation.
Charge as much as you want, wherever you want, and don't worry about it.
No, charging does not KILL the battery. So you need not worry about it.
To these and other posts to the same effect.... I ask of you what data you have to support this? I would expect that making claims of little to no degradation while using a supercharger for 100% of charging would have some data to back it up...
The supercharger taper doesn't get below the rate of a HPWC until around 95%, if I recall correctly. So any supercharging between 0 and 95% will be higher power than home charging. Higher power = more heat = more wear on the battery. Simple as that.
As I said previously, Tesla's thermal management is pretty unique and works reasonably well. However the design only has the cooling loop make contact with the cells themselves at one small point on each cell. So, heat has to wick through this point to be taken away by the cooling loop, meaning the entire cell heats substantially and a portion of that heat is able to be taken away, resulting in a lower average for the entire cell.
Based on testing with single cells, under supercharger levels of charging (~1.5C) the cell heats up super fast. Even at 0.5C (42kW) the cell heats up rather quickly. However, at 0.25C (HPWC levels) the cell doesn't heat up hardly at all.
Heat is a key element in degradation, and more heat is generated inside the cells while supercharging. That's just the way it is.
While Tesla's warranty will cover problems with the battery regardless of how you charge the battery warranty explicitly disclaims degradation. (I forget exactly how it's worded in legalese, but it's there.) So, up to you to keep your battery healthy, and supercharging exclusively is not the way to do it.