You're conflating correlation and causation. Unified URL and search was initially introduced by Firefox (via the awesomebar) in 2008, because they'd observed in user testing that users couldn't tell the difference between search text box and URL text box and were disinclined to learn; rather than continue to retrain users (which they'd attempted with multiple iterations of resizing, new icons, etc.), they unified the features and relied upon the two inputs having wildly different shapes of text to disambiguate.

Chrome followed suit later that year, because by the time Chrome hit the market, awesomebar had demonstrated its utility for end users.