Although this idea is not specifically an idea for stadia itself it would use the same technology.
There has already been a number of posts about keyboard and mouse connectivity to CCU and i am fully behind this. Assuming that this does arrive in some form could the CCU be used as a remote desktop for Chrome OS. The same tech (probably less advanced) could be used. This could be used for word processing etc the same way that Shadow PC current does I believe.
If this was an option available it would marry well with Google docs etc and would make my PC all but obsolete. With the convenience of no updates, instant access to files and no hardware updates it would be something I'd find hard to pass up. Especially if it was linked to the pro subscription.
While I totally agree that having access to a full VM (even if it's just Chome OS) would be awesome, I highly doubt they are going to want to do that with Stadia as it confuses what Stadia is for. If anything, I see this being a future but separate service entirely that builds on the Stadia infrastructure but is not Stadia.