Is that a National Rail obligation or can TOCs decide to have card-only stations - I know Northern have some stations with card-only machines?
It is part of the National Rail Conditions of Travel that cash must be accepted for all National Rail stations.
If the station has a card only machine, with no other ticket selling facilities, then you can get on the train without penalty and pay on the train, or at your destination.
Of course, this doesn't stop some TOCs from assuming that someone who wants to pay with cash at their destination is trying it on and attempting to avoid paying the fare.
The railways are making it more difficult for people to pay with cash, and will no doubt slip in a surreptitious change to the Conditions of Travel when they hope no-one notices.