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Debian apt repos work this way. Everything has hashes or PGP signatures.

It doesn't have to be encrypted to be trusted. In fact, anyone can set up a separate mirror and clients can use it with no concern about safety.

It doesn't offer confidentiality, but it does offer integrity.

You could securely sign the data in a tamper resistant way. Although that would be at least as disruptive to http as https is. And it also can't obscure the specific pages you're visiting.

Cryptographic verification?

Sure, but that would still leave the data open to the world. Not an alternative to TLS.

Most of the content on the web is intentionally open to the world.

But our personal data is not. So much data is potentially made available from an unencrypted HTTP request.

Nobody is saying that personal data should be unencrypted.