Cores in the EU sense do not have anything to do with what the locals think. You are thinking of Victoria.
In EU, cores represent that other world leaders accept the king's claim to own that land, not that the locals agree.
Actually they represent both these things or at least so we've always been told. That's why cores modify revolt risk and taxation for instance.
So the English would love to have a Scottish guy sitting on the throne... No way! And What about Austria when they inherit Hungary? Or Aragon on Sicily and Sardinia. :/
To be fair there are counter examples too. Swedish nobility revolted and threw their legitimate king out of the country due to him being king of catholic Poland as well in the 16th century. Despite the polish king being the son of their previous king they chose to crown his uncle instead.
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