This concept is somewhat applicable to primary hypogonadism, but less so to secondary. One of the posters over at PeakTestosterone has primary hypogonadism and tunes his
TRT dose to achieve normal levels of LH and FSH. Of course because he's primary he doesn't make much, if any of his own testosterone.
In secondary hypogonadism there's commonly dysregulation at the hypothalamus or pituitary. This manifests as a low natural set point for testosterone. If you try to correct the situation with small amounts of exogenous testosterone then the body reduces its own testosterone production. In fact exogenous testosterone provides greater negative feedback than natural testosterone so you end up worse off than when you started. Only full replacement of natural production can raise serum levels in these situations.
In the case of hypothalamic dysfunction it's still possible to "let our body produce what it could", but most would find the procedure impractical. The combination of a SERM and frequent doses of GnRH allows direct stimulation of the pituitary, resulting in endogenous LH, FSH and testosterone, even in the presence of exogenous testosterone.