Consider these:
遅かれ早かれ
良【よ】かれ悪【あ】しかれ
What is the underlying grammatical make up of this ~かれ~かれ
pattern (if any)? Is this pattern productive(i.e. can be extended to arbitrary words)?
The 〜かれ appearing here is the imperative form. I suspect this exact construction is no longer productive in modern Japanese as adjectives are no longer thought of as having imperative forms; however, the dictionary offers this modern rephrasing of 善【よ】かれ悪【あ】しかれ:
よいにしろ、悪いにしろ
So in some sense the abstract construction of "imperative + imperative" to mean "be it ... or ..." still survives. (The "be" appearing in the English version might also be construed as an imperative, but it's probably a subjunctive.) The thesaurus (for want of a better word) lists some alternatives:
For perspective: There are also the expressions
~ろうと~ろうと
~ろうが~ろうが
e.g.
よかろうと悪かろうと be it good or bad
早かろうが遅かろうが be it early or late
I think these expressions are more productive than ~かれ~かれ, although they do have an archaic feel to them.
Also, it might be interesting to know that よかれ is commonly used in the sense "good intentions" or something like that:
よかれと(思って)したことが裏目に出た I did it with good intentions but it backfired on me
~かろう, although slightly archaic, is still sometimes used instead of ~いだろう
それはおかしかろう! (You have to admit) that's strange!