This stumped me for a while, kept seeing “No content types have been subscribed” message even having set up content type publishing and subscription.
Click on “Content type publishing error log” to see the cause of the problem: The content type cannot be published to this site because this site has Document Id Service feature enabled but the content type hub site does not. Please contact the administrator.
Enable the Document Id service on the content type hub site, click “Refresh all published content types on next update”, then “OK”. Run “Content Type Hub” and “Content Type Subscriber” timer jobs. Sorted.
