Because it's an obvious way to get more people to default to Google Search. Just like how IE defaults to Bing. Until recently Google was the biggest contributor to the Mozilla Foundation due to their deal to enable Google as Firefox's default search engine.

There isn't any benefit in Google locking users into their free software if it means users on other platforms can no longer use Google's revenue generating services.

Your point about brand awareness is valid but not really the same as what I was originally discussing (software lock ins). Eg Google's products work fine on other browsers so there's no actual technical lock in however users are encouraged towards Google because of brand familiarity and browser defaults for search and home page.