modal verbs - Tense agreement in the past irrealis conditionals

The following is taken from PEU¹ 123.5:

Could have + past participle can refer to present situations which were possible but have not been realised.

He could have been Prime Minister now if he hadn't decided to leave politics.

We could have spent today at the seaside, but we thought it was going to rain, so we decided not to.

The above two are the examples of past irrealis conditionals.

But I just don't understand why "now" / "today" agree with the past tense (could have been Prime Minister now / could have spent today).

I would think they should be like this:

He could be Prime Minister now if he hadn't decided to leave politics.

We could spend / be spending today at the seaside, but we thought it was going to rain, so we decided not to.

Do these two alternatives make sense? How do they differ from the original ones?

Edit:

Interestingly, as @Fantasier suggested, PEU 259.3 also introduced a similar usage:

We sometimes use structures with would have ... to talk about present and future situations which are no longer possible because of the way things have turned out.

It would have been nice to go to Australia this winter, but there's no way we can do it. (OR It would be nice ...)

If my mother hadn't knocked my father off his bicycle thirty years ago, I wouldn't have been here now. (OR ... I wouldn't be here now.)

But PEU failed to provide more explanations about why this is acceptable and how native speakers think of and use it.

^{1. PEU = Michael Swan's, Practical English Usage.}

Answer

As Geoffrey Leech (Leech 2004) puts it, “Past hypothetical meaning and the use of the modals is one of the most difficult areas of English not only for non-native speakers, but also for native speakers” (p. 127).

I have always thought that the oversimplified rules of conditional use, so common in old-style textbooks and no longer used in linguistics, should have been abandoned long ago. Your question is a case in point. Obviously, traditional rules cannot explain such sentences.

It is much better to think of (what is commonly referred to as) conditionals type 2 as unlikely (Huddleston’s remote) and conditionals type 3 as impossible (Huddleston’s doubly remote), without any reference to present, past, or future.

Trying to keep both analyses, Leech 2004 somewhat struggles and argues that “[t]here seems to be a growing tendency, in fact, to associate the Perfect after a secondary modal purely with ‘contrary to fact’ meaning, rather than past time” (p. 128).

He also observes that in such sentences, when modals are followed by perfect auxiliaries (in the main clause), “the past meaning of the Perfect seems to have been lost” and only the ‘contrary to fact’ meaning is applicable.

Mittwoch, Huddleston, and Collins 2002 - more linguistically oriented - offer a much better analysis (see Chapter 8 in The Cambridge Grammar of the English Language). They call such constructions doubly remote (conditional) constructions. They give the following examples:

[48] i. If you had told me you were busy I would have come tomorrow.

ii. If you had come tomorrow you would have seen the carnival.

iii. If your father had been alive today he would have been distraught to see his business disintegrating like this.

They argue that the perfect auxiliaries express modal rather than temporal meaning (p. 754). Huddleston 2002 (Chapter 3 in the same grammar) adds that the difference between remote and doubly remote constructions is "not very tangible," cf. his examples below

[6] i b. If they were alive now they would be horrified.

c. If they had been alive now they would have been horrified.

To conclude, Huddleston also argues that doubly remote constructions are "fairly rare" (p. 150).