I think it COULD work, but would not be allowed to work in this country. First, you would get objections from the likes of the Daily Wail, and media controlled by an Australian, whining about increased income tax - and the Tories would do everything to try and stop it.
If it did occur, it would need a steady transition over several years - to allow time to improve infrastructure and construct a lot more trains.
Also, it would be best adopted as a scheme to discourage (not prevent) car use in busy urban areas. It would also be desirable to reduce the number of parking spaces in town/city centres, instead providing large park/ride facilities several miles from city centres (with a sensible charge to use them). Getting rid of 1st class and converting space to standard class only would ease some of the inevitable overcrowding on some lines.
Although free (at the point of travel) transport would be expensive to implement, there would be some substantial cost reductions. So no need for ticket selling people or equipment, ticket gates, travelling revenue staff, etc. Plus much less paperwork, no refunds for late running, a lot less work for accountants, etc.