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@Leomonade
It's not just because of reputation, but also the people of his land. They are suffering under his stupidity, which is why she wan't to help them, the status of "wife" gives her a certain degree of authority she can use.
@Ipaat
Divorce wasn't always a thing.
Back then it was crazy expensive and basically only for men, it makes sense because in the past you only married for benefits, rarely for love.
I suggest that you look up the topic, it's really interesting!