This reminds me of when my wife and first started dating long distance - Skype screen sharing movies was our jam
Though I originally made it for me and my SO, it was surprising how many people have told me that they also have done the whole netflix, skype and "3, 2, 1, go" combo. Its interesting to think about things we could make that would better allow shared experience or emotional intimacy with people over distance.
This is pretty much exactly what myself and fiancee did - though for us, the '3, 2, 1, go' became part of the tradition, and we took it in turns to make up 'alternative countdowns' for programmes. Interesting the way that technical limitations can also translate to shared experiences.
Of course, the biggest issue was that netflix offerings in the US were very different to those in the UK, so we'd spend about an hour where one of us tried to find dubiously legal ways to watch a programme the other could watch fine on netflix.