I don't seem to be able to do it and I can't remember if this used to work before.
You can do this, but you have to select either side of it to work. Copying sub-parts of tables doesn't, however, so re-purposing this.
I'm testing on https://en.wikipedia.org/wiki/Manchester_British-Americans . I don't manage to copy/paste the table in Safari, but it seems to work in Opera. Results may vary though.
Will right-clicking on the table to copy it ever work?
Change 265660 had a related patch set uploaded (by Esanders):
Multi-cell table copy and paste
(Ed, I don't understand your edit to the description.)
Change 265660 merged by jenkins-bot:
Tables: Multi-cell copy and paste