I agree that the term “letting go” is a simple one, however, when meditating, I find that term/concept to be useful. The Buddha described five practices to deal with distracting thoughts (MN 20), with the third one being simply to turn away from it or ignore it: “If evil, unskillful thoughts continue to arise in a bhikkhu who ponders on their disadvantageousness, he should in regard to them, endeavor to be without attention and reflection. Then the evil unskillful thoughts are eliminated; they disappear.” While it is better to do the first two (replace it with a wholesome thought or reflect on the harm it causes), one could argue that this third strategy is “letting go”.
Another reason why this simple mental construct of letting go is helpful at times is because it is quick and allows me to rapidly return to the focus of the meditation. In a broader sense, though, I like the concept of letting go because it embodies the idea of renunciation and disengagement. I let the idea fill me, pervade my mind and body, and can then enjoy the pleasant abiding/sanctuary that results.
I do agree with you though, that at other times, it is important to focus my meditation on a specific hindrance. In those times, simply letting go is not enough and then one does need to carefully inquire into the hindrance. But as Buddha mentioned, excessive thought can also be a problem: " If I were to think & ponder in line with that even for a night… even for a day… even for a day & night, I do not envision any danger that would come from it, except that thinking & pondering a long time would tire the body. When the body is tired, the mind is disturbed; and a disturbed mind is far from concentration.’ (MN 19, MN 19 Dvedhāvitakka Sutta | Two Sorts of Thinking)
Thus, meditation becomes an interesting balance between “letting go” at times, and at other times, deeper inquiry. As you mentioned, this deeper inquiry may occur during the fourth tetrad, the dhamma tetrad. However, in the first three tetrads, especially the final steps of each (kaya #4: calming bodily formations, vedana#8: calming feelings/mental fabrications, and citta #12: releasing the mind), “letting go” may be the most effective strategy so that one can then move on to the dhamma tetrad.
I view meditation as a refuge. A mind state in which I can see safety everywhere.
Abstaining, unaroused,
he everywhere sees
security. (SN 4.15)
The first three tetrads allow me to gradually build that foundation of safety and refuge. I perceive safety in my body (kaya), my feelings (vedana) and my mind (citta) through letting go. Then, from this foundation, there is the mental space to explore the dhamma (anatta, anicca, dhukkha), and to apply insight to the hindrances.
With metta,
Nalaka