I noted this when the Met Office started naming winter storms back in 2016 or so. The job I did at the time was significantly impacted by weather, and people completely lost their minds about Storm Anna (or whatever it was). The weather the previous weekend, which was just before the cutoff date for a 'named winter storm', was actually worse, and didn't warrant any mention at all. That's not to say the weather isn't getting worse - it's certainly a lot warmer and wetter than it used to be - but the response to it isn't purely rational either.
From a purely rail point of view, especially post-Carmont, the 'shut everything down' approach is entirely understandable, even to me as an outsider. The rail industry's safety culture is commendable, and we should be aiming for a transport system that has zero fatalities or serious injuries.
The unfortunate fact is, we've built a society where people do believe - rightly or wrongly - that they need to travel, and over longer distances than in even the recent past. Managers might accept 'the train was cancelled' as a reason for missing work once or twice. They won't accept it if it's a week a month for several months. And people won't tolerate being isolated from friends and family on a similar basis.
When the railway is unreliable, people will choose to travel by road. With buses having their own issues, that usually means driving - and someone who's started travelling by car is unlikely to only sometimes use it.
Ultimately, it doesn't really matter whether the railway is shutting down more because the weather is worse, or there's a more risk-averse reaction to the same weather. If the railway wants to be seen as a viable method of transport, it needs to find ways to stay open in all but the absolute worst conditions. I don't know what those are, I'm not in the rail industry. But they need to be found.