I would agree that TDKR is striving for that depth, but doesn't quite attain it. It wasn't as thematically coherent as BB or TDK for me, but it still had some interesting subtextual moments.
Both BB and TDK were comic book pieces too, in my opinion, not any less so than TDKR. I would say The Dark Knight is the strongest of the trilogy for its relentless momentum, insane villain, complex themes and how satisfyingly it all came together. Rises falls short of these things (although, I thought Bane was a great follow-up to Joker). I still really enjoyed it though, and was still able to appreciate so much of Nolan's craft.