The timezones work out great for people in the US, and the museums have nothing to lose since it's all incremental revenue.
One could argue that this would be great for disabled people. Maybe so, but that wasn't what was shown. However, when they hook up a 360 degree high-def camera and feed it through to a next-gen Oculus Rift VR headset, yeah, then we'll talk.
Not going to happen. Public museums of Europe want you to go there. European cities like London, Paris, Madrid and Prague have cultural tourism as one of their main incomes. They don't want to have the experience comoditized.
Also security has enough problems with telephones that robbers use to track the guards if they have them in their line of vision. Add one of those "guard trackers" inside the museum, so they could study their movements and know exactly what they are doing, how much they are, and where they are, their age, their corpulence, the arms they carry, their phisio-phisical state(guards some times are somnolent).