We are a private organization and we will never have public projects. Is there a way to disable the option completely in the product or an entire organization? Inadvertently choosing a public project would be a be a very undesirable outcome.
And welcome to the community forum.
There is currently no way of disabling this option. But when trying to change a private project to public there is some warnings and a confirmation is asked.
And by default when creating a project in a paid organization it will be private.