Kakashi lost his Sharingan for the plot to advance. Madara took it to get to Obito to the Kamui dimension, which led to Kaguya being released, etc
there is a clear plot imoortance in his loss of the Sharingan.
“Momoshiki getting revenge on Sasuke” is cope
It's important to Momoshiki characterisation that he finally gets his revenge on Sasuke, also it's a simple consequence to marge scame battle that took place. Kakashi losing his Sharingan wasn't important to the story, Naruto and Sasuke losing their arm wasn't important either.