I've had a look at Google's docs[1], and it's really not clear to me what Chrome's omnibox offers that Firefox's address bar (or whatever they call it) doesn't.
Chrome, on the other hand, only exposes non-Google search engines through the search engine keyword thingy, which means a user has to actually type "en.wikipedia.org widgets" into the omnibox. Sure, tab-completion will do half the work, but the user still has to remember to start typing "en." rather than, say, "wikipedia".
I know that Chrome (and, indeed, Firefox) allow you to edit those search engine keywords, but that is power-user territory, and power-users can edit their Firefox UI as well. http://i.imgur.com/mS5Ot.png
The reason to keep the search field is people use it I guess. And there would be some confusion once removed.
Typing it into the Awesomebar will do an "I feel lucky" search.