I think that the kind of person people believe Sherlock to be, is actually the kind of person Mycroft is.
I don't really understand why.
When it comes to Sherlock, people just hang on to the "great man/good man"-quote for dear life, repeating again and again how Sherlock says that he doesn't care - but have they ever taken a look at his face? (This is one of the things that I love about your rewatches: how you also describe the facial expressions, not just what's being said and done.) Can anybody believe Sherlock that he doesn't care about the old lady who died in "The Great Game" after seeing his expression during the phone call? Honestly, nobody always means one hundred per cent of what he or she says, so why should Sherlock be any different?
As for Mycroft, people come up with the weirdest explanations. I've actually read a couple of times that he has to be a sympathetic, friendly person who is interested in people because he is a politician. Now, I honestly didn't know that people held politicians in such high regard! :)

I'll let you know my thoughts on your other rewatches during the next couple of days. I think it's great that you invested so much time into writing them, they're an amazing source for every Sherlock fan.