Hello Daizan,
Taigu is bound to have a much better answer than me.....I am running the risk of sounding less fortune cookie like than in my last posting, but here it goes
Striving to not-strive doesn't work....but nevertheless, we are humans so we will always fall into that trap again and again, we might just as well get used to it.
The "playing out" bit can indeed naturally happen by itself however, once a certain level of frustration has been reached. The intellectual insight behind all this sadly doesn't help at all in real life, other than making one feel guilty about still not having reached a point where one strives less.
Let's illustrate this example by using a rather shallow analogy: If you operate in your daily life based on the idea that shopping brings you lasting happiness, you might repeat the same mistake of buying stuff to make you happy again and again.....the Dharma as a practise path for developing deep attention will not get rid of this urge simply through your reading about it...but it might enable you to actually be present and notice clearly what it is that arises whenever your old reactional pattern of equating peace and happiness with something you can buy kicks in again.
There might come a point (or points actually, since this is not a one-off affair), where you will have developed a certain awareness-attention-capacity that might enable you to really experience the frustration of this repetitive circle....after having repeated a certain pattern for thousands of times, you might indeed be suddenly in a position where you can intuitively spot the soft underbelly of dualistic striving: "Wait a second...I've done this a million times...this is bullshit!"
That's how I found the dharma, I had to be so frustrated with my uncountable previous approaches (religious and otherwise) to reality, that the only thing that was left was the Dharma. Other people recognize the greatness of the Dharma a lot sooner

I had to bang my head against every wall life threw at me before I arrived at the Dharma....
When your capacity for truly open insight and attention has become stronger than the momentum of your striving....that's when something will have played out.
Other than the mere technicality of practising the Dharma/Zazen for some time, another big problem is to be found on the level of self-esteem. If deep down inside yourself you don't believe in the possibility that someone like you (and I mean all of us and not you personally) could ever be a "finder" instead of a "seeker"....finding is impossible. Usually being too proud is the problem, but being too humble (Oh silly pathetic me...I could never get IT) is also a problem.
Gassho,
Hans Chudo Mongen