Tell me about public blockchain apps that do not involve objective money or objective identity, which require strict global consensus, why they should be built on public blockchains, and why haven't they been built yet? I'll consider writing a post, when I get back to it, to explain why it does or doesn't make sense

There is the Climate Action Data Trust (https://climateactiondata.org/) aiming to prevent double counting carbon credits by using a public blockchain for auditing.

Countries can keep their local registries, while the neutral blockchain is used to audit across registries.

Objective data, so to speak.