Yes, there are blockchain-based mobile operating systems in development. Some examples include Fusion OS, MOAC Chain, and UBports among others which integrate a decentralized approach leveraging blockchain for increased security and transparency.
As for using ERC-20 tokens or dapps to create a privacy-sensitive mobile operating system through the utilization of smart contracts is not impossible but would take significant development and integration work to ensure it truly encrypts user data and also provides full decentralization while keeping the User Interference uncomplicated. However, blockchain can add an extra layer of transparency & auditability which allows users greater control over their private data that conventional Operating Systems such as Android or iOS aren't able to achieve satisfactorily yet.