Decentralizing the database in a federated structure for anime tracking is a very good idea. Right now I'm using Anitrend that is open source but is only a interface to Anilist.
Like you pointed I think the major challenge will be to establish a solid new shows database entries police(s). Not sure how we could manage that effectively. Governance will be key but you also don't want to be a hostage of this project for your life.
One aspect to be taken in consideration is privacy. I think a lot of people would appreciate to have access to the new tracker without having to share anything about them.