If the advertising screens failed, it wouldn't stop a train continuing in service.
If a route map failed, that could be a problem, but the displays keep whatever is on the screen forever, even without power. That's why they're so good for eBook readers - with battery lives measured in weeks or even months.
Another option might be to have the actual route map as a poster (a failsafe if you like) in the middle and eInk above and below that can put up notes (like the stickers put on now) and maybe an arrow to show where the train is - and direction of travel etc.
There's another technology available right now, but not really used much as yet. Transparent LCD displays. Some slot machines in the US (e.g. Vegas) use them, and Samsung and LG have produced bigger screens for use in shopping malls, shop windows etc.
A future train might have such technology put in some of the windows, either external windows or the glass by vestibules. The passenger information displays would not be separate units fitted in the train, but actually IN the glass.
Vandalism would be an obvious problem, but if I was building a train of the future, I'd certainly be trying to include all of these things - even if when it comes to placing the order, TfL and others would leave all of the boxes for this cool tech unticked!