I'm of those who think that qualifying a quarterstaff as a polearm is a bit of a stretch.
I mean it's a pole alright, but it's missing the "arm" part. As for quarterstaff being usable with PAM, it makes total sense as a two-handed weapon; the staff's balance and relative light weight makes it a fast and agile weapon, apt for parrying and rapid ripostes, trips, feints, etc. That is well represented in PAM. Heck, if there was one possibility of a 2-handed finesse weapon, the quaterstaff would have been my choice.
But 1-handed quaterstaff loses all these attributes IMO, turning an agile weapon into a rather unwieldy one. So I find staff + shields or dual wielding staffs (staves?) more silly than believable. The spear at least has the benefit of having a pointy bit, and skewing with a spear 1-handed has more flair than swinging an oversized baseball bat in one hand that you can see coming a mile ahead. I guess you can hold it at half-point but then you don't have the velocity, leverage, and body momentum to make it dangerous, or at least, as dangerous as a spearhead lunging your way.
...and I know that Gandalf fights with a sword in one hand and his staff in the other at one point in one of the movies, and while I'm usually the first to bring Tolkien in my arguments, this one i find less palatable and believable.
Otherwise, from a purely mechanical perspective, PAM+shield is comparable to dual wielding at level 4, if only a little superior. Average damage is about the same but PAM+shield is 1 AC ahead.
quaterstaff (1-handed) + dueling + PAM = 1d6+str+2 plus 1d4+str+2 plus +2 AC
Two swords +two-weapon fighting + Dual Wielder = 1d8+str or dex plus 1d8+str or dex plus +1 AC
Dual wielding starts losing to PAM once the second attack at level 5 comes in play however, not to mention that it's easier to get one magical weapon than two. That however, may have more to do with the fact that two-weapon fighting in general starts falling behind at higher levels. Two-weapon fighting has the hidden benefit of being Dex-compatible however so there's that... [edit] But then again, shield+PAM has the hidden benefit of being Shield Master-compatible and work with magical shields too. [/edit]
So PAM+spear+shield makes some logical sense and helps the modest-but-dependable spear finding a niche (for whoever isn't a monk). But PAM+staff+shield... Put me in the camp of "cheese".