Except that combining them causes the side effect of sending everything to a third party, rather than just what they are willing to give them. Does the search provider really need to know what url you wanted to go to? Especially given that most of them are greedily saving that information in order to better convince you to buy something you don't want or need at the behest of someone else.

Maybe instead of "which box should they type into" we should be asking why the url interface is a simple text box to begin with.