Provided that a diagnostic zygoapophyseal joint block is successful in diminishing the pain, denervating the joint can lead to a reduction in pain. However, as there are lots of different structures in the lumbar spine capable of nociception, it is very difficult to be certain that the joint is the only source of pain. Add to this central sensitization at the spinal cord level, and you can have pain without any real nociception. In that case the procedure may noy work at all.
Even if it were to work well, it may not abolish 100% of the pain (as there may be more than one level causing pain). And peripheral nerves do regenerate, which in most cases leads to a return of symptoms a few months later.
One concern I have with such procedures is that they also denervate the motor supply to the Multifidus muscle, with theoretically disastrous consequences in the long term.
If all the possible benefits are weighed up against all the possible risks of the procedure, it then comes down to personal choice, I guess.