I guess I'm not super concerned, because I stopped watching TV news a long long time ago. In general they do everything they can to spread fear, and this is just an extension of that.
Does it worry you that this kind of fear-mongering might be bad for society even if it doesn't impact you personally? You might not watch the local news, but many other people do.
It's just corporate media who no longer cares about informing the public in seek of profits. It guarantees a watcher all day to consume ads, on edge about extreme events to stay tuned and consume ads, while also normalizing severity. These things are already put out on TV, Radio, and over many SAME alerts by NWS in the event that there is a real emergency. There is also the easy to read convective outlook.
It's not really about spreading fear, per se, it's marketing. Stations want their weather team portrayed as the most accurate and most dependable with the most cutting edge 3D no 4D no HYPERCUBIC storm tracking technology.
They want viewers to rely on their station alone for weather forecasts simply as a means of ensuring viewership and increasing the value of their ad time, so they make those forecasts seem as critically important as possible. It's the same phenomenon that leads to all news being breaking news.