I don't deny that Cache API was usable from HTTP/2 push. I'm responding to your question asking whether Chrome will obsolete the Cache API because it was usable

I don't deny that Cache API was usable from HTTP/2 push. I'm responding to your question asking whether Chrome will obsolete the Cache API because it was usable from HTTP/2 server push. My answer is no, of course not, because Cache API is unrelated to HTTP/2 push. It's useful for storing resources regardless of whether they're HTTP/2 push'd from the server or fetched from the client. Indeed, the primary use of Cache API is storing resources fetched from a client's service worker.