To faith or gold buy districts is a feature for end game. That is why I say I feel it will be of limited use. If the capital move needs all that and can't work with those cards or wonders that give bonuses to other continents cities, then I don't think they reward that much for the cost to prepare a city for that.
Just because something is there doesn't mean it should be abused. Can you not see how broken it would be to move capitals on a whim? You'd basically get to supercharge cities in no time. There has to be some investment.
Also you can buy districts with gold and faith within 3/4 governor promotions. That's like 2 civics and the government plaza with ancestral hall... and she is encouraged to rush that plaza.
And you don't even need to buy them that early. First few cities can hard build Cothon fine. By the time it gets problematic, it won't be problematic.