I don't think users work that way on phones. Even on my android phone I just search. Now it is also true that the info I am searching for with my phone is quite different than the info I search for with my computer... I don't know... maybe that's the difference... the type of information.
Not really sure... but I am sure that it never occurred to me which search engine I used on my phone. Or even if I borrowed someone else's phone to search for something, I never gave which search engine I was using a second thought. I am absolutely CERTAIN that I have never searched for Google... and then searched for what I was looking for... even with an iPhone I never did that.
I don't know... maybe Google was always the default? Can't remember... but I seriously doubt people have time to "setup" a mobile search. That's not how I work on a phone and I suspect a lot of other people don't either.
Even for maps... I hit maps... if Google comes up... that's what I search. If Bing or whatever comes up... that's what I search. I have never looked for Google maps... or for Bing Maps. Except on the desktop because I think Bing has that perspective "Bird's Eye" thing that's pretty cool. But I never used that on a phone, because it never occurred to me.
I don't know... that's just me. I'm kind of always in a hurry though... ESPECIALLY on the phone.