The entire business model of Google is "Web as a Platform."
Of course they're trying to increase the web and make it better, faster. They're trying to make the web compete with full-fledged Operating Systems. Google doesn't care what browser you use, as long as you're using one that lets them develop their own infrastructure and deploy their own products.
Google has no reason to try and "crush" Firefox. Firefox is irrelevant to them. What they're really after is killing Microsoft, Internet Explorer, and getting their services such as Google Docs, GMail and more into businesses. They don't care about the browser as much as they want to compete in an area where they know they will win. Such an area would be web apps and web infrastructure.
Don't think about this as a browser war as much as a platform war. Microsoft's platform is Windows, Google's is the Web. Google just realizes that if the web was better and more fluent, they'd have a larger market and a bigger piece of that cookie.
That's my 2 cents, at least.