I thought that I had explained the confusion over the terminology at Phab:T139442#2695072.
The current state is this:
The English Wikiquote has hidden a single button related to the Extension:Cite in the 2006 wikitext editor (which almost nobody uses, except a small number of old hands). They have left it visible and functional in the 2010 wikitext editor (used by almost all editors who started editing since 2010, as well as most of the older accounts). And, of course, because of the nature of wikitext, anyone can edit the existing ones or type new <ref> tags manually, even if the buttons aren't there. Or even (as the product manager does) if you're using the original wikitext editor, which has no buttons or toolbar at all.
In the visual editor, the equivalent button is buried at the bottom of a long, collapsed menu. But – because of the nature of a visual editing system – in the visual editor, if the tools don't exist, you can't just type in the <ref> tags. If the tools aren't there, then you can't edit existing ones or add new ones.
The current request is this:
So the Phab ticket (unknowingly) proposes making it possible for users of the three wikitext editors to continue creating and editing unwanted <ref> tags, and for the users of the visual editor to be unable to do the the same thing.
The response is this:
The devs refuse to create this sort of "second-class status" for some users. If anyone can edit or create (functional) <ref> tags, then everyone should be able to do that. If it's possible to create and edit <ref> tags in the 97% of edits made with the wikitext editors at the English Wikiquote, then it should be possible to create and edit <ref> tags in the 3% of edits made with the visual editor at the English Wikiquote.
But the real (reported) problem is this: The English Wikiquote doesn't want anyone to use Extension:Cite. And the product manager is willing to turn off the whole thing, for everyone – wikitext *and* visual editors, on all pages, for the whole wiki. Turning it off will make people stop using it. You can keep citation templates (which are completely unrelated and under local community control). But if you want people to stop using <ref> tags – if you really want 100% of edits to stop creating functional <ref> tags, rather than just 3% of them – then we can kill that software for you in *all* the editing systems.
All we really need to do that is evidence of a community consensus. A discussion in which people say "We don't want any more of those little blue clicky numbers on our site" is perfectly adequate for this purpose.