Well even before we had heard of members of her staff leaving because they couldn't stand Eteri Tutberidze's stubborness, the idea that she will always have the final say on everything, this happened many times for example with choreographers prior to Daniil Gleikhengauz.
I think Plushenko probably offered more freedom on certain aspects (considering he's more of a marketing figure rather than the main coach) and more money, but the big reason why this is happening i think it's some behind the scenes political work maybe from Tarasova or someone else, in order to ensure this new team will have the political push.
Remember that there is that council which Tarasova, Mishin, Tutberidze, Tchaikovskaya and others are all part of, and those are the people who vote on the most important decisions like who's going to Worlds when there is a tie (those are the people who dropped Tuktamysheva out of 2019 Worlds), probably funding as well or decisions like who gets the GP/JGP spots again when it's uncertain.
Cause nobody would want to leave Sambo70 only to disappear 6 months after, right? This could have happened years ago so someone has done the behind the scenes work in order to make that move compelling enough.