Interesting idea! Will not be used by me and I don’t know if it’s to specific for only one or two people. But thanks to the #indieweb all the needed techniques are already there. Especially for static sites – like mine, which is Hugo powered – a constant rebuilding is time & resource intensive and could be a blocking point for such live updates.
I’m a bit shocked that no one has done it before now, and I suspect that one of the pre-existing micropub clients out there could probably add the functionality as a one day project at an upcoming IndieWebCamp.