modal verbs - 'Would have' used alone for unreal past situations, not in conditional

Can I use would have alone like

The situation would have been worse without his help.

The lack of anybody's cooperation would have caused us a lot of problems.

to provide the same meaning as using the third conditional (unreal past situations) like

The situation would have been worse if he hadn't helped us.

?

I've seen this use with other modal auxiliary verbs such as could have, must have in a grammar book. But I couldn't seem to find would have used alone in the book. So I would like to ensure if this is the correct use of perfect infinitives. Detailed explanation would be much appreciated.

Answer

Yes, this is acceptable.

Both your sentences present conditionals; although they are not expressed as formal IF ... THEN constructions, they might easily be so:

The situation would have been worse if he hadn't helped.
It would have caused us a lot of problems if anybody had not cooperated.

The protasis (IF clause) of a conditional may lie outside the sentence at hand; this does not invalidate the use of would:

It looked like the school might have to close. That would have been a shame. = If the school had had to close, it would have been a shame.

All of these uses are equally valid with non-past^✲ reference:

The situation would be worse without his help.
The lack of anybody's cooperation would cause us a lot of problems.
It looks like the school may have to close. That would be a shame.

In fact, most uses of would may be understood as implicitly conditional, though the actual condition implied may be very vague:

I would like a piece of pie. [eg, if you have any or if you would be so kind as to bring me one]
I would be happy to do that for you. [eg, if you were to ask me or if you need help]
I would never say such a thing! [eg, if the opportunity arose or even if I were provoked]

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^✲ I should perhaps note that past modal + have + past participle , although it looks like a “perfect” construction, has nothing to do with the ordinary English “perfect”. It is, rather, the language’s workaround for the awkward fact that the modals can, may, shall, will may be used in their “past” forms with non-past (present or future) reference—which leaves them no convenient form for expressing the same modality with past reference. To accomplish that, we employ the “perfect” construction. It would have been is in effect the simple past of It would be.