Currently, to be able to link organizations to a single paying organization (ie. linked organizations), it requires an active (paid) subscription.
My use-case is that we have an enterprise subscription on our production organization, but wish to have a sandbox organization to test infrastructure as code, creating/deleting sub-organizations, and linking API keys.
In my opinion, developers / administrators should be able to test out managing the org structure in a separate account without affecting the primary "root" paying account structure.