I believe that "the institutions are broken" is similar to "the youth has no discipline, is rude, and our future is doomed": every generation believes it and it turns out we're okay anyhow. I'm not saying that having institutions is a fire-and-forget solution that you never need to worry about once they're established. But generally, we have institutions so you don't have to worry about it constantly. And it works tremendously well in most areas most of the time. Being individually hyper-aware isn't necessary.
It's also an interesting thing to watch from outside the US: there's a lot of arguments that it's the US institutions specifically that are broken beyond repair, willfully being destroyed etc. That may well be true, but it has nothing to do with the news being what they are, we see the same kind of news coverage pretty much everywhere, the actual circumstances don't matter. And we have the same sentiment in Europe, it's always this close to the edge. In my opinion, it's emotional manipulation, but it's really hard to get out of it once it has become a habit.
I'm not sure it's a modern thing either. Here is Thomas Jefferson on the same issue, albeit writing about knowledge of facts, not so much the psychological cost of constant fear: https://press-pubs.uchicago.edu/founders/documents/amendI_sp...