PM at Microsoft here. Live Share not only allows you to collaborate in real time in a lower latency snappier environment but also enables you to seamlessly transition from watching to participating, editing, stepping, and inspecting. The difference is you can collaborate but still operate independently which is not possible with something like a screen share. Screen sharing is great when you want to show your entire desktop or show visuals. Live Share lets you add another tool into your tool chest to better enable concurrent collaboration.

Personally I'd find it irritating, as I do with Google Docs.

This is a neat gimmick but I don't think it'll revolutionise anything or end up being the status quo in the future.

Well Google Docs still is less irritating than screensharing what you are doing in Google Docs via Skype.

I'll give you that :)

I can see it being extremely useful for group projects in university settings...

Pair programming is okay with two people looking at one screen, but once you have more than two people, it really is just a drag. Of course, you can use git and contribute separately. But looking at the same version of the code seems tremendously useful.

When I was at university doing programming, we just sat three people to a machine.