It occurred to me since BHS debuted, Haley's appearances w/ PMJ have been for short stretches, and since she's got a catalogue of 'must hear' PMJ covers already, and only so many performances per show, they (PMJ) didn't bother to learn BHS? (Also, she performed her version at every stop of her US tour already)
It seems Creep & All About That Bass are HUGE numbers for PMJ, outside of Haley (they perform those songs w/ other singers when Haley's not on the roster) and she seems to have an affection for singing 7NA w PMJ there really is no room to squeeze in BHS.
If she were going to do it, my guess was to do it on their biggest show of 2016, Radio City Music Hall, (along w/ Morgan's new cover of "Dream On")...but again, that was a one off, show for Haley until she recently rejoined them. Would've loved to see/hear her perform it in NY at RCMH, but I guess it just made more sense for her to stick w/ Creep, AATB and 7NA
Haley's got an embarrassment of riches how popular her covers are....we still haven't heard PMJ perform Mad World live yet, and in show business, you give the people what they want....
an aside, I recently listened to Habits again, Haley's 1st PMJ cover.... I forgot about that buzz I got when I heard it for the first time (Oh oh ohhhhhh....)....basically, the song/event that preceded this still climbing trajectory Haley's been on the last two years