As said on slack, I would argue that those examples do not exactly completely apply since in the case of Anne she wore titles of several Kingdoms, which means of similar weight and nobility. A kingdom doesn't include another kingdom. An empire like the HRE though, could.
The case of George I is interesting, but again the case is a bit specific (and very convoluted indeed) since George, king of Britain, owns a duchy that holds elective power to the HRE throne. De facto it means that this duchy technically isn't really part of the HRE anymore, but retains elective power... Right? I am interested to know more though, because it may still have been considered part of the HRE de facto...? Interesting case to be sure, which only the fragmented elective monarchy of the HRE can allow since most of those duchies and kingdoms are all very loosely connected to an elected emperor that holds very little power over them.
I think though, that as we spoke about, the Amarr Empire case is quite unique (in an unique fictional setting), where the newly elected emperor loses all titles and family attaches when he gets on the throne, to now be part and head of the Emperor Family behemoth, along with his close relatives. It would mean that Khanid relinquishes technically all claims to the Kingdom crown, and so, the Kingdom doesn't really HAVE TO be integrated, being transferred to his heir.
Now the question would be, would Khanid go for the integration of the Kingdom and force his heir to do so? Would he do the opposite? Would he even more, force his way to the Amarr throne while retaining his other titles?
I can definitely see him doing any of those things..