it's not so much that they deliberately unleash godzilla so much that they probably come to the conclusion that if they can't do anything about godzilla, but he can do something about the mutos that are wrecking havok, then it's better for them to just get out of his way and as said in the trailer, "Let them fight". godzilla is never really "stopped" outside of the one time when he technically was when mechagodzilla turned sentient and crashed them both into the deep ocean depths. eventually godzilla just moves on and leaves people alone for a while until he feels the need to come back around because he can or some monster comes knocking around and he has to go beat the ever living shit out of it. he gets tired after a while and will go away for a while at some point though. it's not something that anyone can make him do unless they have some weird mystic link to him or something like the twins and mothra or the easter island people and megalon/gigan.