> It'd be cool if the browser used this to allow cross-origin caching as well.

As a caveat, there's info leaking here depending on whether the cache hits/misses, so this would need to be opt-in from the cache source, e.g. You set up subresource integrity and also say "allow other domains to load this resource from the cache."

Call it subresource sharing?

Edit: opt-in would need to be on both "sides" (sharer and sharee).