I really like that about the powerlessness of the character and the external source of the suffering as being crucial elements of the woobie.
It's funny, because my first thought was also Star Wars, but not Kylo; Obi-Wan gets woobified very frequently. Personally I have approximately zero emotional investment in Kylo Ren, but that sort of dichotomy in how fans of the character think of him reminds me a lot of attitudes toward the Fëanorians generally (and Maedhros particularly) in Silm fandom; you see at times the same sort of effort to read against the text in order to morally justify the character's actions.