The realized model of having two separate boxes could only ever be "wrong" in a moral or aesthetic sense. This is not the case for mental models, which are incorrect when they do not correspond to reality.
The vast bulk of users would respond either by changing nothing about their behavior because all this stuff is inside-baseball to them, or changing their behavior by resetting their browser's search bar to some other target (for example, I can go into Chrome right now and remove Google from the list of search engines).
At this point, one really has to reach to conclude that awesomebars are bad for end-users without an ideology that doesn't reflect the average user very well at all.
All models are wrong, some are useful. We are debating how useful this model is.