Not everyone, I fear, as I suspect I would hate it (unless I’ve misunderstood how this would work, which is entirely possible.)
Having quoted text marked as such within the post where it was quoted makes sense; it’s necessary to distinguish it from the rest of the reply.
Having text marked within a post because somebody has quoted it further on in the discussion would make no sense to me in most situations. It would add visual clutter and (speaking entirely personally here) would make the post harder to read.
Given the rather random and inaccurate manner in which many of our members use quotes at the moment, I can’t see this adding any value at all in our instance. Yes, it may well work for a literary community - and perhaps others, too - but it doesn’t seem to me that it will improve communication and understanding in the average forum.