You’re wasting your employees time by asking them to keep it secret, when you gain absolutely no benefit from keeping it secret (and in fact are introducing an easy failure point by pretending it’s secret) and you have no guarantees that others are keeping it secret.
> This is one of those situations, for many organizations.
Many organizations just have a blanket policy that you shouldn't be exposing data about an organization's infrastructure unless you need to do it. This is a good policy.
> by pretending it’s secret
No, nobody needs to pretend it is secret. You're missing my above point. There is not a dichotomy between secret and public. It is possible for something to be neither secret nor public.
> This is one of those situations, for many organizations.
And those organizations are wrong.