Like Air Force SERE and search & rescue, a lot of this isn't really justified in terms of per-incident return on investment, but by affecting combatants' senses of the lethality of defeat it changes their payoff matrices in ways that minimize principal-agent problems.

Same as the Great Ghost Dance or General Butt Naked convincing warriors they had magical protection from the enemy, or Japanese, Christian, or Islamic ideas of death at war as an honor bringing afterlife rewards (with chaplains embedded with armies to reinforce the sense of protection against ultimate annihilation), or even a lot of the function of battlefield medics in an explosive age (from a government perspective a multiple amputee soldier is just as much a total loss as a dead one, and costs for ongoing care besides) – shifting some margin of your forces' energies from self-protection to mission success is huge

In support of this, the US Navy seems to have known that the sub was lost almost immediately after it happened. Presumably "the sound was not definitive" because they wanted an excuse for a training exercise, but the fact that they used the location of the sound to narrow the search area somewhat reveals how little they were planning on finding anyone alive.