You have to remember that giant corporations are actually many small teams trying to work on their own problems. So the “shit” to one team may very well be mission critical to another team. Part of the manager’s job is basically deciding when it makes sense for two teams to work together (I.e. let the “shit” through) and when it doesn’t make sense and shield the team so they can focus on their work.
And at smaller organizations “shit” can take on different forms. I’ve seen a lot of “executive indecision” shit. Where the CEO or some big shot leader wakes up every week with a totally different idea and he thinks the engineers should drop everything and start working on it right away. The best managers can talk him off the ledge and let their team focus without even seeing this chaos.
As a manager at a big company, most of the shit I'm protecting my team from is not mission critical for some other team - it's the shit they don't want to deal with themselves and hope to drop in your lap.
For the same reason we end up with shit codebases - a combination of ignorance, incompetence, egos, politics, "just-this-once", laziness, and because sometimes it really is the right thing to do.
I've heard that memorably described as managers either being "shit umbrellas" or "shit funnels".