Earlier quoted context omitted.
Profound has two meanings. You're confusing one meaning ("having great knowledge or insight") with the other ("very great or intense"). "He has profound insights on the topic of healthcare" vs. "Please accept my profound sorrow for your loss".
No. The profound in "please accept my sorrow" is a comment on the depth of your sorrow, something that you are uniquely equipped to describe. "A profound apology follows:" is a comment on how I expect my reader to interpret this message, something I am not at all equipped to describe.
Come on. I get all the backlash against Uber — the outrage they're experiencing is rightly deserved — but this is truly asinine.