This comment would be fine if shortened to simply the first question.
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Without Chrome, Google's business is very dependent on a third-party (the browser developer) who has no loyalty to Google. Long term, it's in google's interest to eliminate such variables in their business.
Products don't need to explicitly produce revenue to be worth developing (and advertising). It's shocking to me how this incredibly basic concept is so far beyond the understanding of so many, particularly on HN. Chrome is a particularly easy case, given that, from its inception, it's pushed people towards Google searches. I've lost count of how many times people have pointed out that Android is a failure for Google because they don't make any money off of it (yes really), completely ignoring the fact that a world in which iOS controlled ~100% of the mobile market would be an uncomfortable position for Google (given that internet activity was moving so heavily towards mobile).
And I do doubt thats the only thing they profit from by people using chrome.