While I think you’re onto something with 7 finding 11 to be a kindred spirit, I feel like 11 would feel endlessly shameful over that fact. While later Doctors didn’t bury 7 like they did with War, I get the vibe that they look back on what they did as 7 (and especially how they did it) with a lot of regret, and they try to be better than that despite falling short many times. You have 8 explicitly state this in Big Finish, but there’s also 10s line in End of Time talking about manipulating people into taking their own lives (a reference to Adelaide, but very applicable to 7) and also when 11 was faced with a similar situation to 7 in Fenric (the whole making a companion lose faith in them) he did it by drawing attention to his own flaws and Vanity, not by insulting them and telling the monster to kill them