This isn't true. Offline functionality is the raison d'être for Service Workers. You can run an entire HTTP request router on the client to respond to requests while offline: https://hono.dev/docs/getting-started/service-worker
If I pitched the idea of having SMB shares work online by shipping a driver that could intercept low level SMB calls and reroute them to a mock SMB server that holds the cache they would have assumed I'd lost it.
Surely the browser could help you a bit more to implement offline sites in a more integrated fashion.
You can of course use the CacheStorage API directly as well (you're not obligated to use a mock server): https://developer.mozilla.org/en-US/docs/Web/API/CacheStorag...
I've certainly seen crazier things though. People routinely include entire copies of Ubuntu LTS in their Docker images to ship tiny HTTP servers.