Content type not available everywhere when setting it to be not visible on the new button

We set up a content type and added to a document library, where we could pick it when creating a document, uploading a document or editing a documents properties.

However when we set the content type to be not visible on the new button, it also becomes not visible when uploading or editing a documents properties. Is there a way so it can be hidden from the new button but available everywhere else?

Thanks