Man of Honour
Some cost but most likely disruption of closing a tube station for a long and sustained period of time (rather than odd night/evening maintenance works). Every new station I've ever been to all over the world uses full-height glass barriers.
Yup. Crossrail will have PEDs (platform edge doors).
The cost is vast. The disruption fairly substantial.
It would take years, and they would have to close stations for long periods of times. Can you imagine the chaos? It's already a nightmare when a station is closed for a few months let alone 6+.
It would be great though. The other issue is more about throwing yourself in front of a train when the overground goes "outside" or overground - as it is easier to trespass there.