With Session Identifiers
There's no guarantee that the server remembers the session identifier. It may have fallen out of cache, or another server may be handling the request if SSL isn't terminated at the load balancer.
The client needs to know the server can resume the session before sending any data, because otherwise a the full handshake process will need to be repeated.
With Session Tickets
Even with Session Tickets there is no guarantee that the server will be able to resume the session. The session key may have changed, or the request may hit another server with a different, misconfigured session key.
Therefore, the client needs to wait for the
FINISHED message before proceeding.