A pike may not be able to pierce plate in a one-on-one duel but it can knock a knight off his horse. And if the knight is charging forward then his own momentum will work against him if he crashes into the point of a pike. Even if the combined force of the knight's forward momentum and the thrust of the pike isn't enough to pierce the plate, which it may well do, it can dent the plate enough to cause significant wounds. And even if the knight is just knocked to the floor, the fall is going to be painful and potentially quite damaging.

Knights could not harm a pike formation if the pikemen held firm. Not only would a sane knight not willingly gallop straight into a sharp point, but you can't make a horse do it either. They always baulk and force the knight's charge to turn away. Then the knights are at a significant disadvantage since they are bunched up and milling around and getting in each other's way while the pikemen are free to poke and stab and pull at them at will, until the knights can get some kind of control and get their horses out of range of the pikes.

If a knight is unhorsed, and cut off from the rest of the knights, then they are vulnerable to getting pinned down and finished off with a thin blade through an eyehole or underneath the groin.

The point of the knight's charge is not to actually hit into a pike formation, which is suicide for a squadron, but to scare the pikemen enough to make them break and run. A running man is easy prey. But if they hold their ground the knight can't do anything and pike can actually dominate the battlefield. Once Pike regiments started getting consistently disciplined enough to hold their ground against knight charges this strength became obvious, and Pike started taking over the battlefields of Europe, with knights being reduced to harrying, pursuing, and reconnaissance forces rather than the main front-line shock troops they used to be.

Pike blocks didn't consist of only one rank of spears being leveled, but of several (anywhere between three and five, depending on the length of the pike). Now, assuming that the pikemen are just standing there, and that the have the same spacing between files as the armoured soldiers opposing them, then the men-at-arms need to grab hold of and/or push away between three to five pikes before they can engage with the first rank of pikemen.

These pikemen, not wanting to die, will be thrusting their pikes towards the men-at-arms, which not only makes it harder to grab the pikes, but also means that the men-at-arms are going to be hit by the pikes at some point. Shorter pikes might be able to be aimed at helmets or even the hands grasping for the pike shafts, while longer pikes will probably strike with a reasonable degree of randomness due to the flex of their shafts.

Now, once the first rank of your men-at-arms succeeds in imobilising the pikes of the front rank of pikemen, they need to work out some way of passing control of the pike shaft to the man behind them, or he will need to go through the whole procedure all over again. The second rank of pikemen, meanwhile, are now able to thrust at your first rank of men-at-arms, who must now repeat their previous maneuver.

At this point, if you're facing the Spanish or the Swiss, you're likely to be hit in the flank by either another block of pikemen or by specialised anti-infantry troops from within the block itself.

Here's the real problem, though: pikemen generally didn't stand and let infantry charge them, they either initiated the charge or counter charged. It's not exactly easy to force your way through multiple layers of pikes during a charge. If you are knocked down by the impact, you'll want to pray that your side holds and doesn't get pushed back, or soon you'll be trampled by pikemen and find one of them trying to force a dagger through your visor or any other gap he can find.

pole arms don't just include spears, they also include all shorts of choppy and slashy weapons. With the leverage of the pole one of these weapons could do some damage though the armor of the knight; maybe not penetrate the armor fully, but enough to be noticed. Add a hammer head or a pick head and you basically have a can opener.