Who knows. After all, "tradition" hasn't stopped the British from changing, and it makes things so much more difficult when physics departments are teaching metric, but Americans still prefer miles, gallons, and pounds.
And everyone still calls it "imperial units."
And there's that word: imperial; derived from "empire". And are Americans really bothered by the implications of this word, let alone the fact that they off-handedly call it "Imperial Units" and are proud to use them?
I think that most Americans likely don't even think about it, unless and until they are faced with having a choice (or at least seeing the contrast) between inches, feet, and yards and millimeters, centimeters, and meters. Then it's, "Those are metric, these are imperial." (Although some do call them "American" units, just like some people call what they speak "American".)
However, why not use the other term for these units; the historical term for these units?
Yes, say it with me: Av-wah-doo-pwah.
Okay, maybe I can understand the reticence that some Americans might have with choosing a "French" word, conveniently forgetting (or being ignorant of the fact) that many of the words that they use are French words (just not so French-sounding). It also helps that American English spelling tends to hide some of the more "egregiously French" words, like center (instead of centre), rapid (instead of rapide), maneuver (instead of manœuvre), etc. So, maybe if we changed the spelling to something less "French-looking":
... yeah, I don't think too many people would adopt its use.
And then there's the problem of generalizability. Avoirdupois refers only to the weight of something, and so can only really be used to describe the system of weights, but not of volumes or distances.
I guess, then, that the terms pounds, yards, and gallons will remain "Imperial", and slowly change over time to "American" as the US continues to become the isolated case of a hand-me-down from Roman times that became standardized some 1400 years after the Romans left the British Isles.