And the first thing webdevs did once this became widely available, is change their apps to cache-bust their code; between that, and the short release periods in webshit ecosystem in general, and security and privacy considerations messing up things as usual, the promise of users mostly hitting just local cache with any marginal request, never materialized.

Without content addressing how do I know that whoever holds the cache hasn't tampered with the content?

The integrity attribute of the <link> element lets you provide a hash to ensure the content has not been tampered with.

Interesting. Is this common? Like, is there some way to enable it on my LAN so that when I become disconnected from the internet I can still browse pages which were cached by other devices on that LAN?

It's part of the HTML on the page. It has nothing to do with your LAN.