DevOps is not about startups, DevOps is about avoiding the pitfalls of big companies who completely fail and leave all of their employees jobless by focusing on all of the wrong decisions and initiatives.
It's about outlawing cowboy coding and other bad habits that people pick up as hobbyists, and intertwining business and technical objectives reasonably.
Why is a full-stack developer important? Why is eroding the difference in responsibility between Dev, Ops, and QA important? Because traditionally along these boundaries have been opportunities for individuals to absolve themselves of responsibility. More than anything, DevOps is about not living in that world anymore.
Some people won't survive outside that world. Those who want to will read "The Phoenix Project" by Gene Kim.