google paid 1 billion dollars for a search deal to Mozilla with ~30% mkt share. If google had never built chrome, Mozilla share might be 50% or more today. The search deal would've been commensurately more expensive.
The point is, google doesn't have to pay for search engine placement for a chrome user.
I'm not sure your caveat is needed -- on a new installation the first thing Chrome does is ask you what search provider you want to use, you're just as free to pick Bing as Google.
That's a rather significant difference, you know.
But control over a given user's browser has incredible potential value for Google. Controlling both client and server means that you no longer have to sacrifice performance in the name of standards compliance (so long as you have a standards-compliant fallback mode for other browsers). What that means if you're Google is that a visitor using Chrome can 1) cost you fewer resources, and 2) walk away with a smoother, more satisfying experience.
Does Google currently take much advantage of this potential? I can't say for sure. But we are talking about a company that omits the </html> on its homepage in the name of performance.