I was just ranting, sorry if I offended anyone of if the post was out of context and not required
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In shows with families with the female as the head of the house (not male, because they are very less interested in kitchen politics and just give reactions and yell at people, unless it's MJ from Beyhad 2, who behaves like a Sasuma, himself), it's always shown that the mil either hates the male lead/takes time to gel up to her/doesn't express her love for her dil.
GHKPM actually helped me realize me why this formula works time and again.
Bhavani is the head of the house. Karishma and Sonali have no particular alliances in the house, they hide behind the strongest player. Ninad and Omkar have no opinions of their own and will say to whatever Bhavani and Sonali have to say, respectively. For the sake of this post, let's say Shivani isn't that warmed up to Sai, she likes her, sure, but needs more time to understand the toofan.
So, only, and only when Bhavani will warm up to Sai, will the kitchen drama will grow slower. Because, she is the instigator and the controller of the arguments. She manipulates people around her to hate/like someone.
Like Maham Anga in Jodha Akbar or the mil in Diya aur Baati Hum, Maham continued to hate Jodha, and it did sorta reflect on AkDha's relationship (haven't been a follower of both the shows, but know some bits of it) and when the mil started being affectionate of Sandhya, there was a bit stability in the relationship between Suraj and Sandhya (again, not 100% sure of this claims though). But, I have followed Shaadi Mubarak and Naamkaran, where Kaushala has class bias and hence hates Preeti, thus does everything in her power to weaken Preeti, which will affect every relationship around her (her daughter sorta has given up on her relationship with her mother, no thank you very much, Kaushala) In Naamkaran, Shweta could manipulate Avni till Bebe was unsure of her, but after Neil's accident and recovery, Bebe grew fond of Avni and was always on a lookout to make sure Shweta doesn't harm the couple. Bebe doesn't tolerate Shweta's trash talk about Avni, similarly, Bhavani will defend Sai once she starts getting closer to Sai, hence affecting her dynamics with the entire Chakram Chavan family. Also, after Bebe accepting Avni, the kitchen politics took a backseat and they introduced the new villian.
So, Bhavani will affect SaiRatKhi a lot. The dynamics of the trio will be sorta manipulated by her biases (Pakhi) and till Bhavani actually starts appreciating Sai, Sai is in for madness of the Chakram Chavan family and neither will the show progress.
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Again, just my opinion, but thought of posting😆 Lemme know how wrong I am🤣