Google doesn't care, financially speaking, if Chrome or Firefox does better in the marketplace. They care about the eyeballs that Firefox, Chrome, and any other browser can deliver to Google ads.
Advertising is not their product, it's their revenue stream. Their product is _everything_ that sits between a user and monetizing an ad. Just look at what they have done from an engineering, offensive and defensive position here. It's all about that ethereal space between users and monetization. That's the battlefield, and they want all of it.
They need FF because when Chrome dominates, FF needs to be a viable competitor. With Bing, it would be worse off.
That and that they can use Chrome to lock people into Google services in the future.
Oh no, not more Chrome proves Google is evil...
The only thing I've seen from Google that is a move in this direction is that it will share the oAuth cookie between Chrome Sync and google.com pages to auto login if you're already logged into the browser.
I don't see how Chrome "locks people into Google services" any more than simply enabling them to get there faster (V8, SPDY, etc).