This is a rather odd question but how come during both the Phalanx period and later the Pike and shot era there wasn’t a strategy of having soldiers trained to destroy pikes, either by being incredibly well armored and using that to just run in and pull the pike away, or using a weapon to simply chop the tip off. I know that some Phalanx formations were designed so that other pike users could stab to the sides of them but how in the blazes would that work again say a shield wall manned with people with either swords or axes, better yet how come Pole-arms such as poleaxes weren’t use to dismantle them, after all with a poleaxe you could cut the tip off the pike but still not be in stabbing distance for them?
One of the main problems of fighting a pike formation, whether a Macedonian or Daidochi sarissa pike formation, a Scottish schiltrom or a Landsknecht or Swiss pike block is that the formation is designed to present a large number of pike points to the front, making it very hard to fight or struggle with an individual pike - while you would be grabbing a pike and trying to yank it from the man holding it (who could be holding it with both hands and not wanting to let go of it) many of his compatriots would be stabbing at you with their pikes.
And to get close with the man in the first rank holding a pike, you would need to not only pass his pikepoint, but also the pikepoint of the four men behind him (and probably all the men next to him and them as well), something which would be very hard to do.
The Romans only managed to deal with the Macedonian pike-line at Pydna 167 BCE when it had pushed them back to more uneven and broken terrain, which caused the phalanx to break up in parts, and allowed the Romans to rush in and fight the Macedonians in close quarters, where their short swords and good armour put them at an advantage.
The German landsknechts and Swiss mercenaries did create a corps of special soldiers - the Zweihändermann or Döppelsoldner (two-handed man or double pay man) who wore heavy armour and wielded a huge two-handed sword who would push into the enemy pike formation and bat pikes aside with his sword, crack pike-staffs and attempt to push all the way into the formation and use his sword to whack as many enemy pikemen over the head as possible. However, this was a very dangerous position to be in, and it is debated on whether two-handed indicated the large man (they had to be heavy to push into the pike formation), the two-handed sword or the double pay the men received as an incentive to take the high risk. The chief objective of such men were to disrupt the enemy pike formation, allowing their own pike formation to best it.
The Spaniards devised a similar tactic, but used lighter troops, so-called Rodeleros, men equipped with a steel buckler and a sword and good armour, who would either attempt to dive under the pikes or use his buckler to push them aside to enter the enemy formation and attack the pikemen, disrupting the formation and allowing the friendly pike formation to win the push-of-pike battle more easily.
The problem with cutting off pikes is that the sarissa was generally 4-5cm thick and made of very hard (and heavy) cornel wood, while renaissance/early modern era pikes were often out of ash or oak and similarly thick - it is just not something you easily cut off, especially as they are held aloft and would be decently flexible - cutting at them would bring them down to the ground and make them flex, but not cut through them like you would with an axe to a static object (such as a standing tree). Swiss pikes would often have iron reinforcements running down from the point 50-80cm down the pike-shaft, making it even harder to damage the pike.
As gun powder weapons continued to improve, the zweihändermann, doppelsöldner and rodelero made way for artillery and arqebusiers and later musketeers to disrupt the enemy pike formation, which would peak at Breitenfeld 1631, where Swedish mobile light artillery and double-rank salvo firing devastated the heavy Imperial Tercio formations.