Well… the client knows which resources are already in its cache. The server does not. You just suggested that the server should always send resources that client almost certainly already had cached, which is wasteful for everyone involved.
> So with HTTP/2 push you just push the whole package and the client tell the server if it already have some of the files.
That doesn’t make sense. Once the files have been pushed, the bandwidth and time has already been wasted. The client doesn’t get to tell the server anything in that scenario.