You'd be surprised how few people in software care that you can work a whole stack. Business people don't like to deal directly with programmers because they don't like hearing all the jargon, and managers love assembling dream teams of specialists because it makes them look good. QAs, on the other hand, love a generalist.
I'd say a true full stack dev is someone who can always get to the bottom of a problem. You can earn a lot of respect that way without stepping on other people's toes.