I have set up a couple of custom content types and associated custom columns via the Content type gallery and published these successfully.
They are available for me to add to my Site Pages or document libraries just fine. However, after the initial creation and implementation on my sites, I changed my mind about the need for one of the custom columns and deleted it from the content type and custom columns in the Content type hub, then republished my content type.
However, after I built a couple of further sites, I've discovered that the content type that is coming in still has the original custom column that I deleted from my content type despite it no longer being in the central content type hub site collection.
It's really annoying because I then have to go into each individual site collection and then clean up the content type to get rid of the unwanted column. It somewhat lessens the usefulness of the central content type gallery.
Can anyone else in the community confirm if they are having the same problem before I put in a Service Request about the issue.