Totally agree with this post. I think your analysis is spot on about his appeal, and I have the same preferences; a flawed Batman who can be gruff, but who isn't totally alienating and can still reach out and admit when he's wrong.
I don't know if it's a distinctly modern thing, but I find it interesting how popular the anti-hero always is. I can think of so many characters who fit that Batman trope who are often more popular than their sunnier, more likeable counterparts.
Vegeta from DBZ
Dr. House from House
Rick from Rick and Morty
Downey Jr.'s snarky Iron Man
It has its own trope category too, with other related categories:
http://tvtropes.org/pmwiki/pmwiki.ph...fferableGenius
"I'm a competent hyper-intelligent dick" is just all the rage. Sarcasm rules.