> Why is Google so afraid of making a standalone application to run on desktops and not in a browser?

There is a big difference between "doesn't see the value in the added cost" and "is afraid of".

> Then you wouldn't need your browser open to use "OK Google"

Chrome supports running in the background on startup (and prefers to do so), so conceptually there is no reason anything that can be done in Chrome that doesn't require on-screen UI couldn't be done without needing any application "open" (at least, without the user taking the step of opening an application.)

Seems to me that, both from a strategic perspective and a UX perspective, that's a more natural progression for conversational search than a separate standalone desktop app.

Given how much work they've put into web apps and stuff like NaCl, I don't think Google sees requiring a browser as any sort of downside.