That was the intent based on the original unveiling.
Unfortunately, Wave was never given a chance to replace anything since it was a stillborn project that barely exited the launch phase.
If anything, we all learned that invite only soft launches on something that is expected to replace a service that is ubiquitous is not a very good idea. Early invitees got in, panned it, and by the time it went live, everyone already had a preconceived notion as to what Wave wasn't.
Is this the real purpose of Wave or is this the purpose that came out because it was misunderstood?