There are five (very simply accessible) different choices for Safari on iOS.
But if you switch to iCabMobile on iOS there are TWENTY-FIVE search engines to choose from.
I think you might as well be asking regular consumers to root their device so they can use whatever Apps from outside the App Store, or whatever search engine they want.
Also, even for a technical user, there is simply no way on an iPhone to change to a new search engine not already on a tiny list, and from talking with hundreds of consumers, I have not talked with a single non-technical person who could work out themselves how to change their Safari search engine to even one of the 5 limited choices, let alone a new option.