As an aside, I've trained a bit in the use of a polearm (though not a pike, really). Anyway, I sort-of don't entirely agree with the fluff of how the feat works anyway, pike or not. It's pretty slow to turn a polearm around (even a shorter one) and yet it's pretty quick to thrust it twice. At any rate, rather than saying that the feat wouldn't work with a pike, I would just have changed the fluff to represent a quick weak-thrust as the bonus action, seeing as they consider the bonus action 1d4 to be balanced with the regular attack of other polearms, it doesn't seem to make much of a difference. But that's just me.
(As an aside, I can't imagine how anyone would use a quarterstaff without using both ends, which 5e doesn't model at all, go figure.)