@Hazeyln
That is a nice fantasy you hold. While sex is very important, it's not a panacea for every problem.
However, the main prerequisite for a scenario where sex can support a relationship, is for a relationship to exist in the first place.
The main characters in this story do not have a relationship. Just because they are married on paper, it doesn't mean that they have a relationship.
The ML got roped into marrying her by an imperial order. MC got told to do it by her family.
ML isolated her, impoverished her, and abandoned her until she agreed to sign the divorce papers.
MC was unwilling to divorce, not because she gives a damn about the ML, but because she knew her family would sell her off like livestock as soon as the divorce was formalised.
So after experiencing what it feels like to be destitute, she conceded to agree, on the condition of being allowed to have a lover.
She wouldn't even have been "cheating" to begin with, because again, they did not have a relationship to cheat on.
All she wanted to do, was indulge in some extreme escapism where she could experience an actually satisfying sex life, before she inevitably gets sold off to some old geaser in dire need of a heir or daughter.
She's so starved for affection she's literally crying at the chance to actually have a more exciting physical experience than what she has experienced so far.
I don't know about you, but a marriage that only makes people miserable, emotionally stunted, and desperate, does not qualify as a good marriage in my book.