Does the Government not pay for anything other than the railway and hospitals for kids?
If that's the case, I am starting to believe Labour was possibly right after all about the cuts being too hard.
As for advance tickets - why not just make it possible to pay extra for travel insurance. Or, assuming travel insurance wouldn't cover you simply waking up late and missing your booked train, add an optional fee that allows you to excess your ticket. Say £10 (the normal admin fee).
How many people would pay the £10 if they fully intend to get their booked train, compared to those who would buy an advance ticket but know that they might get another one? Remember, the fee only allows you to use the value of your ticket against another ticket (but I'd argue that you'd be allowed to use a railcard if you had one, so getting the same discounts as buying before travel) it won't just let you travel on a later train for free. Or, if it did, perhaps only if travelling within a certain time (e.g. 60 or 90 minutes) - and forfeiting any seat reservation.
If someone did a careful analysis, I'd bet that the industry could actually make a bit of money out of this and score LOADS of PR points. Many people would not pay the £10, and be happy as they'd make sure they were on time (as you would be for a flight). Some would be worried that circumstances could delay them (e.g. a meeting, late overrun of a sporting event) and gladly pay the £10. If they get their train, they're £10 down. If they don't, they're not landed with a full open single.
Advanced tickets with this fee wouldn't now be as cheap, but as it would be an OPTIONAL charge, it would not need to be included in advertisements. Another win.
People would then, hopefully, learn that if they skip that optional fee then they've got absolutely NO COMEBACK whatsoever. I know they don't now, but at least the industry is giving them a fair chance - and, as I said, they'd likely make a nice easy £10 on lots of ticket sales with no loss whatsoever.
I might even suggest this to ATOC, although hopefully they're reading this.
BTW, £10 was a figure plucked out of the air - it could be more or less, or even vary on the service, time of day, number of passengers etc. It wouldn't matter to train staff, as the ticket would be marked as allowing an excess or not, so that could be decided by the TOCs and retailers.