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

After making a few on-chain mistakes in the past couple of days, I am pretty sure something like that will never exist on L1 without compromising its integrity.

On L2s, yes, but it won't be truly permissionless. An example would be Nightfall.