It seems that most TOCs already do, although admittedly its normally for travel after the storm not before.
What it should be is a decent period before and after (at least two days), and it should be a national decision. People genuinely get stuck between a rock and a hard place when they have a long through Advance involving multiple TOCs or worse a set of split tickets.
I'm thinking of, say, someone having a ticket from e.g. Lancaster (let's stick with it) to Brighton where a storm affected the north of the UK, as is not unusual. Avanti might declare "do not travel", but Southern are going just fine. That passenger needs an easement for their whole journey or a sequence of splits, and that doesn't universally happen.
Similarly, it's no use saying "travel at the same time the next day". Quite a few people who got stuck last Sunday will be weekly commuters to London who would need to travel early Monday rather than their usual Sunday evening, for instance.
So in essence what I would propose is that the rule should be that if any TOC declares "do not travel" for whatever reason, any ticket, of whatever type,
that was purchased before that declaration and has validity on that TOC should gain Anytime validity during any period of say two days before and two days after for the entirety of the journey, and that should also apply to a sequence of contiguous splits other than them remaining routed via the split point.