You could have a heroic doctor but nobody’s full time job is ‘hero’.

Anyone who is regularly engaged in heroics would be a full-time hero, in the same way that anyone engaged in full time medical practice would be a doctor. In Snowden’s case, he effectively quite his job at Booze-Allen and became an advocate for dismantling of the surveillance state effectively full-time. He stopped drawing a salary as an intelligence analyst and focused all his time on assembling, distributing, and propagandizing the nature of the PRISM program and the need to end it.

A hero is a term that’s useful in a novel but some people wanna cosplay

It’s a term that is used to describe an individual engaged in a heroic effort on a sustained basis. To your point, you could easily describe a Doctors Without Borders volunteer or a volunteer firefighter as a hero-as-full-time-job. Depending on your ideology and the individual’s circumstances, you could also describe a civil rights advocate or a military operative or a journalist as a hero.

It’s a weak descriptor, because just calling someone a “hero” doesn’t explain their heroic status. Whereas, calling someone a doctor pretty clearly illustrates how they’re (presumably) spending their time. But “Hero Journalist” definitely conjures an image that is different than “Paparazzi Journalist”.