There should also be an "Added via admin panel" option. This way we can let admins use the Content > Integration screen to create a header e.g. on a specific profile, but if "Profiles" is unchecked, then there are no controls to create a new header when visiting a profile that doesn't have one.
For the "Profiles" option specifically, I think there should be a Usergroup setting, so that only members of specific Usergroups can have a header. While it can be cool to let a member feature a wiki page on their profile, this feature was created mainly to show wiki biographies of notable members. A usergroup setting would allow us to say who is notable and who is not.
For clarification of "Wiki content container", I suppose that you mean:
For each content-type, have additional options for integration containers that would be supported by that type.
For example, it should be possible to show a profile integration as either a header OR a tab, but it wouldn't make sense to show a thread integration as a tab. This capability awaits a fix for the "Position" regression, however.