You can actually do something similar with an Interrail Pass [1]. It's a train ticket valid in all of Europe for 1 month for €407 if you're under 26 or €532 if you're older. Still, pretty cool!
EU is also planning to give Interrail tickets to to all young EU citizens, I hope it becomes a reality: http://www.independent.co.uk/news/world/europe/interrail-pas...
Europe can be cheap as much as you want, hitchhiking and youth hostels are safe and available pretty much everywhere. You can even visit expensive cities like London for about 20$-30$ a day by sleeping in a hostel and and eating fast food(or even cheaper if you do groceries and cook in your hostel).
I really love what we have in Europe, it would be a huge tragedy if it all collapses back to the divided and hostile Europe.
A train ticket for kids paid for by unwilling tax payers is little more than bribery and propaganda. It's disgusting, they can't win the hearts and minds of the populace so they insinuated themselves in schools and now are outright bribing kids.
I was pro-stay, but some of the stunts the EU are pulling to get kids to believe in EU federalisation are disgusting.
Giving young people means to travel is not brain washing, it's actually the opposite as they can actually go to that country and see what it is all about so they would be less susceptible to propaganda. It's like public education but with no teachers to push an ideology(it's just a ticket, doesn't come with a guide), I would say that if EU manages to pull this of it would be a great public service.
Edit: Making an experience available to everyone isn't exactly propaganda.*
*unlike that extra £350m pw going to the NHS
I will be more than happy to contribute to that with my taxes to give opportunities to young people to become more open minded.