Thank you all so much for the responses. I appreciate it a great deal.
This question was initially phrased in a way which was determined to be too subjective, so this is an attempt to make this a very clear question with a factual basis, and to which I believe that the answer is, "No."
By "ought to make a careful writer avoid the phrase" I mean that it is considered by at least some usage experts to be problematic. Perhaps they consider it trite. Perhaps they consider it infelicitous wording.
In his essay/review "Tense Present: Democracy, English, and the Wars over Usage", Harper's Magazine, April, 2001 (also reprinted in expanded form in Consider the Lobster and Other Essays), David Foster Wallace says:
But the really distinctive and ingenious features of A Dictionary of Modern American Usage involve issues of rhetoric and ideology and style, and it is impossible to describe why these issues are important and why Garner's management of them borders on genius without talking about the historical context2 in which ADMAU appears, and this context turns out to be a veritable hurricane of controversies involving everything from technical linguistics to public education to political ideology, and these controversies take a certain amount of time to unpack before their relation to what makes Garner's usage guide so eminently worth your hard-earned reference-book dollar can even be established; and in fact there's no way even to begin the whole harrowing polymeric discussion without taking a moment to establish and define the highly colloquial term SNOOT.
...with the footnote:
2 Sorry about this phrase; I hate this phrase, too. This happens to be one of those very rare times when "historical context" is the phrase to use and there is no equivalent phrase that isn't even worse. (I actually tried "lexico-temporal backdrop" in one of the middle drafts, which I think you'll agree is not preferable.)
Is there anything which ought to make a careful writer avoid the phrase "historical context?"
FWIW, Garner's Modern English Usage, 4th edition, does not appear to object to the phrase; in fact, Garner uses it several times (e.g., "Rime still appears for rhyme on rare occasions. But unless it's in a historical or jocular context (or there's an ancient mariner involved), use the modern spelling...").
After others' comments and further consideration, I believe that the answer is "no."
Source: Gardner doesn't seem to have a problem with it; see above. None of you think there is anything wrong with it.
A more definitive answer would at least require a review of all of the major usage guides, I suppose, but I suspect that one of you would have pointed it out if there are usage guides which object to the phrase; for that matter, you would know that the phrase is best avoided when possible.
This is more lit crit than usage, but my best guess is that Wallace is sort of playing a joke on the reader here, by apologizing for the use of a non-widely-objectionable phrase and claiming to assume that the reader (who is probably at least a bit of a language/usage/grammar nerd) also finds it objectionable. The reader, like me, might think, "Geez, I'm a bit of a language/usage geek, but I'm no DFW, but here he is apologizing for using a phrase which I didn't even know was a problem. How come I never knew there was a problem with "historical context," and what is the problem? Because there must be a problem, or Wallace wouldn't apologize and assume the reader objects, too."
TL;DR: I got trolled by DFW.