A staff can indeed be a great weapon against many opponents, give it a spiky tip and it can be used as a spear two. It’s the ultimate peasants weapon. Also, I would like to insert the psychological effect of a unit of full plated knight with tower shields and swords, backed up by spear wielders and behind that a row of crossbowmen, I have faced that in a LARP, (tough luckily usually being one of the crossbowmen) this is seriously fearsome. the sound of them marching itself is scary. And very few tactics that work against it.
Also, considering two handed weapons. They indeed leave you open to counters now and then, but those counters had to be swift. So when you are wearing a very thick suit of armour (full plate) those quick counters would only rarely be hard enough to hurt you.