The thing is that a Google Mail early invitee could collaborate with everybody else via the pre-existing standard of SMTP email. They felt special because they got a new web UI, told their friends about it, generated hype, which then made the invites feel even more special, etc...
Google Wave had no existing standard to leverage, making it 100.00% useless if you couldn't invite EVERYBODY you needed to collaborate with. But you couldn't! You weren't allowed! They had to wait for an invite. Days? Weeks? Months? Years!? Who knows!
There was a snowball's chance in hell that this marketing approach could possibly work for a collaboration tool like Google Wave, but Google knew better. They knew better than every journalist that pointed this obvious flaw out. They knew better than every blog post, Slashdot commenter, etc...
It was one of the most spectacular failures caused by self-important hubris that I've ever seen in any industry.
https://www.newschoolers.com/news/read/Got-Google-Wave-Invit...
https://bolesblogs.com/2009/10/13/get-your-google-wave-invit...
https://googlewaveinvites.weebly.com/
And so on: https://www.google.com/search?q=%22google+wave%22+%22invites...
I never used any of its collaboration features, just looked at them. I did use it as a friendly-for-non-geeks version of IRC for a group of people that lived in three separate cities as a virtual watch party for LOST. And for that, it was spectacular even if it was painfully slow on a netbook (so was everything else, but it was cheap and light and worked).