Key points to remember before we talk about the specifics:

Sengoku period armies were very fractured.

Levies were often raised, trained, and conducted battle with those they were familiar with, and often in the service of a specific lord/bushi/retainer/etc.

Massive formations of men regimented and trained to operate as parts of a large, greater, singular force were rare.

This meant that massed coordination between different allied units/formations/levy groups was difficult and required heightened investment of time, money, and manpower.

Sengoku period armies were often mixed arms.

While individual units numbering a few men to perhaps a few dozen or even hundreds could all be armed similarly, often on the battlefield, soldiers and men would have mixed in with one another.

Leaving pikemen (or any other kind of formation) completely alone would be the same as leaving them open to attack. You raise this possibility when you mention that it would be a simply counter to have dedicated soldiers rush in low while pikes were raised or distracted or whatever.

By the late sengoku period, pikemen would have been accompanied by soldiers with portable shields, firearms, spears, knives, and swords. If anything, the pikemen accompanied the formations with firearms.

Those who had access to a significant number of fire arms, which most serious contenders in military conflict during the late Sengoku Period did, often used them as the core of their forces and tactics.

Pikes were generally meant to dissuade cavalry and infantry rather than to outright kill or beat them down

Pikes, when held in tight formation, are very difficult to maneuver around very much. Holding them in place while moving or bracing in formation is something pikemen everywhere drilled into their bones. Actively thrusting quite often, while in tight formation, would have been a tough job for most pikemen anywhere.

'Pushing' with pikes is a sounder tactic when thinking of the longevity and need for a pikeman to remain fresh for as long as possible while in formation, enduring the stresses of battle (which is key since the strength of the pikewall is in, well the wall holding together).

But pushing with pikes, especially when confronted with other pikes and other infantry formations, relies heavily on the depth of the formation for mass and momentum. More pikes also don't hurt! While sheer numbers can add mass to a formation, it's more effective and efficient for it to be a sizeable number of soldiers who are well disciplined and will hold under duress.

These requirements generally rule out these tactics for many pike formations that many Sengoku tacticians would have had at their disposal because of the first bold I mentioned.

All these factors combined allowed for this unique use of the pike to be an viable tactic on the Sengoku battlefield

Pikes are solidly made from wood and Japanese ones are no different. A good hit from that would shake most anyone, wearing armor or not. If they consistently fractured from a heavy horizontal impact, it would render them unusable fairly quickly in the course of a battle, which of course is a real possibility.

But even if this were true, it would beg the question of why it was strongly suggested to use the pike in such a way in a contemporary account (though written by an anonymous author).

Putting that aside, pikes can indeed be used this way and were generally effective because situations and conditions that made such tactics vulnerable did not exist due to the various qualities of the standard Sengoku battlefield.

Put very bluntly, this was just another method of fighting and was usable if for no other reason than that it did not consistently disadvantage the user.

Also, these bouts of swinging pikes would not have lasted very long.

Swinging such a large weapon would have been extremely strenuous and for it to continue would require relief soldiers to switch into the front line (a very difficult thing to pull off) or require the participants to break off and regroup. After breaking off, they would reassess and rejoin in the same manner or do something else appropriate to the situation.

Lastly, swinging pikes, particularly in unison, is effective for the same reason a very orderly pike square advancing steadily is effective:

The apparent discipline and experience have large effects on morale for both sides.

As you say, pikemen lifting up their pikes would be extremely vulnerable, and for quite a period of time, to enemies keen on rushing in behind the points and striking hafts. Leaving yourself vulnerable and relying on allies to protect you/braving greater personal danger allows a greater degree of flexibility in action and is apparent to both comrades and enemies.

A comparison could be drawn to pike squares advancing steadily even into the pike points of an enemy formation, or the orderly phalanx where each soldier helped cover his comrade beside him.

Morale is never to be ignored when considering the viability of tactics. Hence why some of the greatest military thinkers in history devised tactics involving great big lines of men firing at one another only a short while after the conclusion of the Sengoku Period conflicts.