I am not a native speaker of English, but I studied in the UK and lived there for a long time. To me, at least in the British usage "Vodka and water" refers to a cocktail. Otherwise one would say "Either vodka or water..." in your example. But then again, I might be biased. However, I think it's important to clarify where one comes from in terms of orientation. I am absolutely anti-chomskian. To me, analysis starts from what people acutually say and not from what they might say but never do.

I am not a native speaker of English, but I studied in the UK and lived there for a long time.

I'm a native speaker of US English, and these nuances of unusual agreement are areas known to differ in US and UK English, so that's worth being aware of in the discussion. I can't comment on UK English, and it might be different from what I'm saying (or even narrower dialectal variation).

To me, at least in the British usage "Vodka and water" refers to a cocktail. Otherwise one would say "Either vodka or water..." in your example.

True, confusing example. It's hard to come up with a good one for what I wanted, but just assume the context makes sense. Like I said, where you're trying to avoid drinking too much alcohol without water. Or if you go to a party and they're offering both (and only) beer and wine, and most people have a preference and drink only that, but then you say "Come on everyone, beer and wine is best!"

However, I think it's important to clarify where one comes from in terms of orientation. I am absolutely anti-chomskian.

I've been trained in a Generative framework, but I also find Constructional approaches to be useful. In my research I'm looking into ways of taking the most important aspects of both. (I don't think it's an either-or answer.) Admittedly it's much easier to find fault with both theories than to be sure about which aspects of either are definitely correct.

To me, analysis starts from what people acutually say and not from what they might say but never do.

That's complicated-- in principle I agree with you (and reject 'armchair' approaches to things in favor of gathering real data), but it is also important not to overlook more peripheral types of usage in favor of only common expressions. And this is actually where Construction Grammar excels!
Personally the biggest problem I have is that I think many armchair style Generative analyses are not clear enough (or imaginative enough) about the contexts in which an utterance might be used, and therefore miss generalizations about grammaticality. I'd rather think of it not as whether a sentence is, outside of context, grammatical, but what it would mean if it were to be used. So something like we're describing here does have a clear intuitive meaning to me, even though it's a very rare sort of expression. (But as a whole, certainly not unused. Just rare enough it's hard to think of specific examples. Searching in a large enough corpus would surely generate some results under the right parameters! This isn't just hypothetical.)

I agree with "wine and steaks is good", but then again, to me it implies an omission along the lines of "(a meal with)...".

I don't understand your insistence that there must always be a source construction (rather than as one potential analysis). As I've said, I believe it is citing a grouping as a general concept, which is in that sense not countable, and therefore gets singular agreement. It's grammatically like a direct quotation, shielded from external grammatical relations.
In this case, "a meal with" is not the appropriate substitution because it is a more basic concept than that. Maybe it's a snack. Maybe it's a smell. Maybe it's a look in a photo. Maybe it's a recipe. Maybe it's a taste of a meal but not a full meal. Or if you change those two items for some other combination it might be any other number of things. Just because you can paraphrase it doesn't make it ellipsis. It may be analogical to diachronic ellipsis (as you made a case for earlier), but not every combination like this needs a specific source construction.

Otherwise how would justify it?

That's easy! It's just a concept. Like an infinitive form of a verb with no tense, this is an "infinitive" form of a noun phrase, with no number. It's not being counted, so the grammar isn't sensitive to that either. It's a concept, like "mac and cheese" or "steak and eggs". It's not a set phrase (binomial) like those, but it works the same way because "wine and steak" is a pairing rather than a plural group of two. If you really need it to come from ellipsis, then I suppose you could claim all of this is something like "[a set of] wine and steak", and the set is what gets singular agreement. But I just don't have that intuition, although I admit that such an argument isn't really testable or falsifiable. Either "ellipsis" or "abstract concept" would give us the same data.

The reason for my strong intuition is because of minimal pairs like the following:
"Red wine and steak is delicious."
"Red wine and steak are delicious."
Those have very distinct meanings to me, exactly as would be predicted from what I'm saying about the two distinct analyses. The second is sensitive to grammatical number specifically because it is semantically different from the first. The second is a list. The first is an idea.

"An idea" is no linguistic parameter, whatever approach one might embrace.

Indeed! That's why I'm saying this isn't a grammatical issue, because it's semantic agreement.

Let's agree to disagree.

That's fine. One aspect of this discussion that confuses me, though, is that my explanation seems better suited to a constructional approach, and if you weren't explicitly stating that you don't adhere to Generative Grammar, that's exactly how I'd be reading your analysis. But maybe if I interpret your explanation in a broader functional way, where "ellipsis" doesn't mean something in a derivational sense, we're really saying the same thing. But I still wouldn't call it ellipsis, and either way I don't know how we'd test for that.

German requires the subject to be expressed. So "what do you mean?" would be "was meinst du"?. More and more users write "was meinst?" by omitting the subject. This is a case of ellipsis. The extent to which this will cause German to become a pro-drop language in many, many years is not predicable.

That example makes sense to me. But I get a completely different intuition for the English examples we are discussing. (And note that in English you can do basically the same thing as in German conversationally. e.g. "Got it?")

Ellipsis is not derivational, no (also cf. Evans).

I don't see that as a meaningful term then.

It's a process by which speakers start dropping units at whatever level.

That's not what my intuition is for these constructions.

Then define and motivate semantic agreement, please

Compare:
"Your family was nice."
"Your family were nice."
The speaker is expressing a different perspective on the number, or indeed countability, of "family". It wouldn't make sense to me to say that one is elliptical (or both), although you could claim something like "the members of..." without any direct evidence, if you insist on the vague idea of "ellipsis" in a non-derivational sense. But that could apply to literally any construction that has unusual forms, just imagine some extra structure that would make more sense and say it's "elided".

In this case, speakers are mentioning the idea of "two doctors" (or "red wine and steak") or whatever, and then discussing that conceptually rather than referring to countable entities.

I have a strong intuition about this, and just saying "there's something missing" isn't evidence against it. I'm not sure how to falsify either approach, except inasmuch as mine predicts much wider productivity whenever speakers wish to speak this way, and that's what happens. Since there is always going to be some structure you could claim is elided, that's not a way to test for this. And arguably everything is elided in some sort of cognitive analogy in describing the world. But I don't see that as explanatory in this case.

I would be willing to consider this a sort of Constructional derivation where the internal grammar of the construction is irrelevant because it is being mentioned rather than embedded. If that's "ellipsis" then OK. But it's not literally eliding anything. It's just mentioning a concept.

This isn't a specific grammaticalized construction. It's possible in any context where citing/mentioning a complex NP is pragmatically appropriate instead of referring to individual entities. Literally any sentence/construction you can imagine would permit this, although of course rarely does English mark grammatical number so that it would be contrastive. Basically it would only ever appear with subject NPs. I don't know whether other languages behave similarly.

If you were organizing a photo shoot for some kind of advertisement and trying to decide who to put in the photo with the product, and you wanted to explain to someone about who to put in the scene, would this be appropriate in Italian?
"Il bambino e la bambina è perfetto."
If not, Italian is different from English. If so, wouldn't the same sort of mentioning-rather-than-referring apply?

Actually going back to something you said earlier, we could think of this as a sort of grammatical metonymy: we refer to the singular concept of a collection of entities in the singular because that is how they are pragmatically relevant.

Sure. But how can you "prove" a construction? Regardless, having a specific construction wouldn't mean that in the general case this isn't just a 'citation'/mentioning form.

Still, I don't think either of us has a direct counterargument to the other's analysis, or any way to (potentially) falsify either one. So we can just leave both as plausible explanations.

You can prove a construction by showing that it only works with some restrictions (see Goldberg).

Well, in the general sense, I don't think there are restrictions on this use of singular agreement for plural-structured concepts. But perhaps in this particular case there are exceptions to that. I didn't mean that you shouldn't enumerate them here. I just meant that in general it's fine if we agree to disagree, because the different proposals we're making don't seem to make any different empirical predictions.