There's an interesting article from Christian M. Mackeprang that tries to provide some definition to the term "full stack programmer" and what it really means to the job market.
Back around 2013, the term Full Stack developer started to come up in job descriptions and blog posts. Companies were realizing that hiring developers with expertise in only one language just wasn’t enough anymore. A web developer that can handle a variety of tasks and environments is considerably more useful, and was starting to become the norm.
He talks about the combinatorial explosion the number of possible technology combinations can cause and how the usefulness of specific posts/resources is dwindling because of it. He then talks about "hackers" as "antifragile programmers" being the ones that enjoy the exploration of the tools and systems and are not bothered by change. He also suggests that developers need good skills in time management and setting expectations to prevent too much "exploration time".
He finishes out the post sharing thoughts about redefining the roles we're actually looking for an the individuals we want to fill them. He offers pointers about gaining context around issues, understand tradeoffs and doing what other people don't like doing to make your way ahead.