I don't think this is true. I'm pretty sure I don't ever pronounce the h in historical if I'm coming into it from "an." "Anistorical." The "i" takes care of the "h."
Also "a history" becomes "[ə:]istory" (but definitely not "an history") and "the historical" becomes "th[ə]istorical." Definitely no "h."
It gets dropped in other situations, too. "Speaking of wh[ə]distoricallyappened..." I can't be sure when I don't drop it, other than when the word is bare. Fairly boring black middle-class midwestern accent.
> if you're pronouncing the "h" (which everyone does).
You can say "an 'istoric", but that's not what we're talking about. The overcorrection is "an historic".
That also isn't specific to "historic", for example you can say "an 'ouse" but literally nobody says "an house".