I think a lot of that "match story telling" ended with the BAM! one shot finishers that there's usually no coming back from (i.e. Stone Cold Stunner, Pedigree, Tombstone). And Burd did hit the nail right on the head with the talk about the Horsemen back in the day and the Minnesota Wrecking Crew before that. They were notorious for picking one body part and working it over the entire match.

I can't speak for nowadays because, as I've stated many times before, I haven't even watched a segment of Raw or anything for about 4 or 5 years now.
I aint lyin'...