"Do not travel" is a fad beloved of the modern railway which forgets that it is a public service which has no business dictating when the public may or may not travel.
Put yourself in the operators shoes:-
There are no or very few trains running
There are more people already stranded *on* the network than you reasonably have a hope of sourcing replacement transport for.
You’re expecting potentially tens of thousands more people to show up to commence journeys.
What advice do you give?
A more friendly way of putting it would be "There are severe delays in excess of four hours. If you travel, please expect your journey to take many hours longer than normal".
Some people might need to travel, or they might be going away for the weekend and might be prepared to put up with a severe delay if it gets them to where they want to go - eventually.
But this is the point - it may not just be 4 hours. It may be 8, or 12. Where do you draw the line. Because at some point there is a crossover where “the railway” first has to enact its duty of care to those already stranded on the network for 4, 6 however many hours; over the hundreds/thousands pouring onto station concourses trying to travel as well.
There is not a customer-base sized fleet of coaches and taxis waiting on call to move everyone who wishes to travel; particularly from a station the size of Waterloo. As such, and as has often been the case in the past, the operator advises against travel. It means there is a fighting chance of those who ignore such advice actually travelling, and that the scant resources remaining can handle the load that is already there.
Consider the alternative - everyone come and travel, then midnight arrives and there’s 8000 people on Waterloo concourse and the last trains of the night have all run?
The truth of it is the public won’t react strongly enough to “friendly”.