Is seems that verb forms as "would have been, would have had, would have done" have no name and are automatically treated as if clauses. Here verb forms are confused with sentence types that contain if-clauses.
"will be, will do" (will + infinitive) is future tense,
"will have been, will have done" (will + infinitive perfect) is future perfect.
Some call the two tenses simply future 1 and future 2 or F1 and F2.
"would be, would do" (would +infinitive) should also have a name and
"would have been, would have done" (would + infinitive perfect) as well.
I call the two verb forms simply C1 and C2 (conditional 1 and conditional2).
The poster has the view that "would have been" is would + present perfect.
That view is totally wrong. Such misconceptions happen because in English grammars the conjugation is presented with six tenses:
Simple tenses: I do, I did, I will do
Perfect tenses: I have done, I had done, I will have done.
I think it would be better to include C1 and C2:
I do, I did, I will do, I would do
I have done, I had done, I will have done, I would have done.
C1 and C2 are not seen as tenses, but only as moods just like the subjunctive. But as "would" is grammatically the past tense of "will",
C1 and C2 have of course a tense character, too.
C1 and C2 can be used alone, without an if-clause.
Yes, that would be fine. (Referring to now or later.)
Yes, that would have been nice. (Referring to something in the past.)