I totally agree with you. You have convincingly debunked this whole meta-grammatical argumentation here that the so-called "potential subjunctive" was ever used in this particular context in Latin. "Would that I want red wine" (the force of vinum rubrum velim) is a wishful prayer to gods to restore one's lost appetite for red wine. In an independent clause, all by itself, it does not translate to English "I would like red wine" but rather "I would like to like red wine (again)" or similar.
Velim studentes tacere = "(If it was up to me, I) would (like) that the class shut up"; here, velim commands an infinitive, this is not the same as a direct object. Scio quid velim = "I know what I want" (i.e., what I would like); here, it is not independent but commanded by scio, which is the prototypical scenario for the subjunctive (aka conjunctive).
If you find examples of independent velim + direct object in Latin literature, anyone, please provide them.
Yes, but classical Latin does not use the subjunctive for politeness. Independent uses of the subjunctive are reserved for other functions: https://www.thelatinlibrary.com/101/Subjunctive1.pdf.
This link seems to list such a usage, but I can't find it anywhere else. https://classics.osu.edu/Undergraduate-Studies/Latin-Program/Grammar/mood/subjunctive/independent-subjunctive
Yes, there is a potential subjunctive, I'll agree. But I just don't know that I've ever encountered it being used that way. More like wishing for things that potentially could be true...ala "Would that it would rain today!" I don't know. I might be fighting an uphill battle here.
An idiom in Plautus when a person or a god is leaving or ending a conversation is num quid vis? (e.g., Menaechmi 327, 548). The indicative mood. It has the sense of "Do you want anything else?" num expects the answer no. Leumann-Hofmann-Szantyr (Lateinische Grammatik, 331) discuss uses of optative subjunctive diachronically and write: "Der Gebrauch wird später häufiger auf seine größere Verbreitung in der Volkssprache läßt wohl auch seine Häufigeit im Romanischen schließen." Cf. potential subjunctive (333-34); hortative and jussive (335).
psyduck99, the examples given in Lewis & Short (p. 2009c) are part of a larger syntactic structure that uses the subjunctive in subordinate clauses, not on its own. It's possible that Romans employed the subjunctive in the way DL teaches with polite requests, but the evidence indicates that they made requests in other ways, not with the subjunctive on its own. Please share with us examples from classical Latin, say Plautus or Apuleius, if you can find them. I cannot find any. MagistraKate has done a service to push us to reconsider the assumption DL Latin makes in such cases. Where in classical Latin do we find an optative subjunctive for an attainable wish in a request of something from someone?