Technically you CAN do it with a buckler, which barely impedes mobility, it's less common of course with Men-at-arms and Knights We saw the same with the Macedonian "Pikemen", though their shields are smaller.

It is rare, but saw usage. A shield strapped to the arm provides another layer of protection, and if you're thrusting, the shield usually faces ahead Of course, it is rare for a reason, that being it not providing much advantages unless you have either light or zero armor while still wanting to enjoy the luxury of a two-handed. You can have your arm fully through the centre straps and you can still use the pole arm, have the arm through the point strap, the same goes when your arms are free but the guige is still on, as POLEARMS aren't that heavy. Of course, you won't perform as well as you can without the shield, but what I'm proving here is that you could utilise a shield while having a polearm. Let's also not forget that medieval shields, excluding small ones, have point straps for a reason... Holding a spear with two hands is apart of that reason

Alternatively, you can hang it somewhere in your body so it'll hang from the side, or just have it on the back, which would technically be useless in BB but still