The myth that you can’t build interactive web apps except as single page app

Can someone explain what the service worker strategy accomplishes that plain old http Cache headers don't? It saves a (almost zero weight) network roundtrip, but feels like it's re-inventing the entire wheel for that small (I think) optimization? Am I missing something?

that they can be used to compute stuff locally

I imagine ideally we want user choice of where the computation is happening. if on a mobile device I'd save battery in exchange for network latency

but in a desktop computer I'd rather do as most local computation as I can