It's hard to miss the larger stories -- they intrude into discussions and conversations. If that story is something I perceive as not useful to know or engage with I'll state as much. This includes most crime and political stories, to the extent those focus on crisis de jour, immediate and personal impacts, horse race, or some orange running its mouth off.
I'm more interested in deeper undercurrents. My guiding question over the past seven or eight years has been "what are the Big Problems". And information that doesn't address this isn't particularly interesting.
Specific major stories are. I've been following hurricane Dorian, for example, though my entry point to that wasn't news, but the https://earth.nullschool.org weather visualiser, which shows interesting phenomena. And Dorian showed up initially as a minor swirl just off the coast of Venezuela, then developed rapidly. Then it started turning up in news mentions.
I occasionally catch On the Media's weekly deep-dive into major stories of the week, or longer. That's about the right frequency for me to catch up on news, and it's no longer every week.
Mostly I'm looking at larger themes and patterns that repeat through history. Models, frames, context. Philosophy, history, systems theory, cybernetics.
Focusing exclusively on the new and now takes away from that.