>Safety is accomplished by effective security, not secrecy.
This seems to depend on your threat model. Two threat models were explicitly mentioned here - terrorists, and contentious public debate.
But it seems a third threat model, and the most important one given that nukes are anti-nation-state weapons, is to prevent nation state adversaries from knowing with certainty the location of those nukes. In which case, secrecy is still a necessary component of nuclear safety, or more specifically, deterrent effectiveness.
I'd imagine it's more of a defense in depth approach. Why do your adversary's work for them? Unsophisticated adversaries (ie. random anti-nuclear agitators) might be dissuaded entirely due to the lack of information, and even sophisticated adversaries would have to take time and effort to verify those fingerprints and make sure they have the right spot. Unless there's a compelling reason to make the information public, I don't see why they would.
And let's hope it stays that way, because it's the one thing that's keeping the world from going up in flames.
If I were the supreme commander of a nuclear power, I wouldn't even want to know where the enemy subs are. I'd make sure the military isn't trying too hard to find them. That's because A in MAD stands for "assured". Nuke-carriyng submarines are often billed as first-strike weapons, but arguably their main role is being a backup - an assurance that, no matter how effective your first strike is, you are going to be glassed in retaliation. So, your submarines check the enemy, enemy submarines check you, and the standoff continues.
If you can credibly threaten to detect enemy nuclear-armed submarines, then the enemy has a strong incentive to launch a first strike immediately, before you've completely neutered their subs.
This seems to depend on your threat model. Two threat models were explicitly mentioned here - terrorists, and contentious public debate.
But it seems a third threat model, and the most important one given that nukes are anti-nation-state weapons, is to prevent nation state adversaries from knowing with certainty the location of those nukes. In which case, secrecy is still a necessary component of nuclear safety, or more specifically, deterrent effectiveness.