Why is the salt washed off the cabbage in kimchi but not on sauerkraut? All the videos I have seen always wash the salt off the Napa cabbage in kimchi but they never do in sauerkraut?  How come?  Is the brine necessary for fermentation?
The initial salting draws water out of the cabbage, otherwise the kimchi tends to get soggy/mushy.  As you mention, it is frequently rinsed off after the initial salting.  If you listed the ingredients that follow, I think you will see that there is quite a bit of salt re-introduced.  The recipe I use, for example, includes, soy sauce, fish sauce, and salted shrimp, among other things...this creates the brine necessary for lacto-fermentation and preservation.