You contended and provided proof that SL and self explanatory mathematically produces the same result. And I concur with this.
If the two of your statements are accurate, then hedging must do the same.
However, re-quote myself:
Mathematically looks the same, but gambling is not about that. .... An opportunity to move the bet off is given by hedging. Or play with an other range. .... Hedging is to prevent losses. SL is to realize it.
You somehow can't see this, and if you are lucky, you don't need to.
Since the price gets transferred to the other direction.
Slimming for 95% - non losing for 5%. Knowledge and expertise does not lead to success. Simply luck if everybody likes to deny it.