For me, Wave had one very strong use case: collaboration and discussion intended to result in a persistent document. Forums, mailing lists, e-mail, etc. are great for discussion, but they are generally ephemeral. Documents are persistent, and with Google Docs can be created collaboratively, but the communication channels around them are weak. You're limited to distracting in-document text, limited comments, or entirely out-of-band communication e.g. e-mail. With Wave you could have the document, editable by anyone, and embed discussion in it and around it. You can discuss a point, updating the base document as discussion converges. It's a brilliant medium for group brainstorming and drafting.
While I definitely agree this would have worked as a great collaboration tool, anyone I tried it with just did not get it, and we ended up using it as a I'm-seeing-what-you're-typing chat box.
That use case alone is enough to make me miss it.