Apple did switch to Bing at one point. The default search engine in Safari is likely just a matter of money to them.

Apple already competes with Google in some search verticals, for example if you ask Siri to find a pizza restaurant, you will get an iOS pop-up with results that link to Yelp for reviews and Apple Maps for directions.

I don’t see Apple competing directly against Google in general-purpose search. But I could definitely see them expanding what iOS does “natively” to include Siri handling more queries itself rather than punting out to Google results.