This is also why Google Voice exists.
Google is serious when they say they want to search everything.
Google is willing to give away these dressers for free because Google makes money through the dresser advertisements, so the more time you spend with your dresser, the more advertising opportunities they have. Thus Google wants to make a better dressing experience for you because ultimately it turns into more revenue for them.
Next up: Google Life, helping you do more and reducing your need to sleep.
[1] Wild assumption, but I expect that the numbers will bear this out.
That said, I haven't actually tried to do any work on Wave, so I can't speak for its usefulness. As a pure email replacement, I find it comparable to Gmail, minus the inferior keyboard shortcuts in Wave.