D&D 5E Polearm Master + quarterstaff...+ shield?

[ph0rk]

Eh. You can probably strike with close to the same force given a whole-body windup and an inanimate target. The issue with trying to use a quarterstaff one-handed is brought into focus when you consider what happens after that strike.

Yep, you gain advantages rebounding from either a miss or a hit with two hands you simply don't with one hand. That's why two-handed lever weapons like a greatsword aren't really slow at all.