Can a hypothetical "could" main clause stand on its own without an expressed conditional?

I have been reading Meaning and the English Verb (Leech, Geoffrey N. 2004). I like its systematic treatment on tense, aspect, mood, and modality. I think it's a must-have for any advanced ESL learners. It's just amazing and extremely accessible, really a perfect complement to Practical English Usage by Swan.

But only one thing I still feel uncertain about is whether could can be used alone without adding "if-clause" to express irrealis thoughts. I know it is true of would(e.g. it would be fantastic to get to the moon), but I'm not sure it's also true of could or might.

Meaning and the English Verb §183

HYPOTHETICAL POSSIBILITY. Used hypothetically, could and might are substitutes for may in expressing factual possibility (see §121):

There could be trouble at the World Cup match tomorrow. | The door might be locked already. | Our team might still win the race.

The effect of the hypothetical auxiliary, with its implication ‘contrary to expectation’, is to make the expression of possibility more tentative and guarded. Our team might still win the race can be paraphrased ‘It is barely possible that…’ or ‘It is possible, though unlikely, …’.

Meaning and the English Verb §186

To conclude, the following sentences illustrate this multiplicity with examples of seven different meanings of could:

#1, #2 and #3 are omitted here.
#4. Hypothetical equivalent of can (= ‘possibility’) (cf. §176)
The house is one of the most beautiful that could be imagined.
#5. Hypothetical equivalent of can (= ‘ability’) (cf. §176)
Do you know anyone who could repair this clock for me?
#6. Hypothetical equivalent of can (= ‘permission’) (cf. §176)
I’d be grateful if I could borrow your electric drill.
#7. Tentative equivalent of may (= ‘factual possibility’) (cf. §183)
The weather has been terrible up there in the mountains. You could find climbing very difficult.

The last meaning is rather more anomalous than the others, as it shows could extending its range of meaning into the epistemic territory of ‘factual possibility’ which is the domain of may, not can.

I would think Leech is making clashing points here. Isn't the usage of could in the three examples in §183 identical with that in #7? If so, why does Leech say #7 is more anomalous? or, to put it another way, why does Leech separate #7 from #4 and #5?

I would think #7 is the most common usage of could. Is the usage of #7 derived form #4 or #5? For #4 and #5. I would think they are just the same as:

The house is one of the most beautiful that can be imagined.
Do you know anyone who can repair this clock for me?

What are the unexpressed conditionals implied in #4 and #5 respectively? If we used can, would any nuances be suggested? Why bother to use hypothetical mood there?

I would agree with you that there are implicit conditions/hypotheticals involved with using "could," whereas "can" is more of a binary "yes/no" describing individual capability.

Sure, I can imagine a house ... but an architect could probably imagine a better one;

I'd also suggest that "may" implies a preference/allowance for one option over another, whereas "could" is more ambivalent about the outcome.

Can: has the ability/knowledge/skills to do something.

P1: Can you fix the clock?

P2: Yes, I can ... I have the skills.

Could: This is a possible option.

P1: Ok, then could you fix it please?

P2: Well, I could I suppose, but I'm rather lazy.

May: likely to lean toward a particular option

P1: I may be inclined to pay more if you decide quickly.

P2: In that case, how can/might/may I be of service?

(Yes, this is all rather ambiguous & interchangeable ... Sorry, I have no references or grammatical rules to cite - just my opinion).

Given that could refers to a hypothetical situation, how can that situation be expressed?

Could is a modal auxiliary verb. It is one of the four "Diamond" modal auxiliaries:

• can, could, may, might

Diamond modals all express the logical modal Possible.

The other five modal auxiliaries (called "Square" modals) all express the logical modal Necessary:

• will, would, shall, should, must

(Diamond and Square refer to the logical symbols ⃟p = Possible (p), ⃤p = Necessary (p))

The point to make here is that all modals refer to hypothetical situations.
Either something is possible, which means it's not known, a guess at best;
or it's necessary, which does not guarantee its existence either.

Think about it -- the least hypothetical sentence below is the one without a modal:

He's in the back ~ He must be in the back ~ He could be in the back ~ He might be in the back.

So there's nothing special about could here.
It's true that the habit of providing a conditional clause to go with a could clause
is extremely common and very effective. But it's not a rule of grammar; it's just one strategy
for communicating; one that's particularly useful in writing, where context is all-important.

Thus, sentences with modal verbs in them can stand alone; and could is no exception.
That answers one part of the question.
The other part is "How does the hypothetical context get expressed, then?"

There are a lot of ways in which this is done.
Mostly we simply accrete context as we go along in a conversation, referring back to things that've already been said (though not in the same sentence, or even by the same speaker, most of the time). There are many other large-scale phenomena, as well; however, I'll mention only one other here: Presuppositions.

A proposition is said to be presupposed by an utterance if
denying the utterance cannot deny the proposition. I.e,

• Bill realizes that the earth is round.

presupposes

• The earth is round.

And so does

• Bill doesn't realize that the earth is round.

For comparison,

• Bill believes that the earth is round.

doesn't presuppose the earth is round, and neither does

• Bill doesn't believe that the earth is round.

Technically, realize, which presupposes its complement clause, is a Factive predicate.
Factivity is just one kind of presupposition "trigger"; there are hundreds, of many varieties.

Presupposition, along with other things, falls under the rubric of Pragmatics, not Grammar.