The somatic path to pitch control
The shakuhachi is an eminently tunable musical instrument. There is no reason why it should not be blown at the correct pitch at all times, with all kinds of music. Yes, the mouthpiece is a bit of a wild animal but it can be brought completely under the player's control. It takes time and a lot of attentiveness to many physical aspects of playing, as well as careful listening.
Modern shakuhachi are made so that if you blow strongly and efficiently, whilst maintaining a good posture, your sound will be somewhere in the ballpark of near-correct pitch. This is only the beginning though. Very slight movements of the head will change the pitch, as will slight differences in embouchure and breath. As a player, one has to become hyper aware of all these nuanced movements and their effect on pitch, because that is the process one goes through whilst actually performing a piece.
Good pitch is as much a touchy-feely thing as it is an aural recognition. It is very useful to learn pitch control on one main instrument, a 1.8 length. This facilitates the understanding of pitch and pitch intervals on longer and shorter flutes.
When you are on pitch at A440 for any given fingering, your body and breathing will be arranged in a certain way only associated with that good pitch, which you can learn and reproduce at will. You literally 'feel' the pitch in the breathing and in the physical relationship of the flute with the body. Our job as players is to be able to revisit that arrangement over and over again for each note, until good pitch and the somatic feeling of good pitch are recognized, and both can be accurately reproduced at will.
Good tsu-meri feels a certain way, in the fingers on the holes, in the posture, in the passage of breath, as does a good 'hi' pitch for example.
So, practically speaking, how do we make this happen? The best way is to play music in unison with your teacher, and listen for their pitch. In the absence of a teacher, the tuning meter is really helpful..
Find a tuning meter that has good strong visible pitch indicators, like LEDs, flashing arrows or a large swinging needle, and position it next to a score on the music stand, so that you can see it with your peripheral vision. While playing a simple piece, adjust your pitch according to the meter's indication, without compromising your posture in any way. At first, this is challenging, especially for those who are relatively beginner players. But slowly, with much practice, you will begin to recognize the physical feedback signals that tell you all parameters are correctly arranged to yield the right pitch.