I think that Apple would only consider building their own search engine if they had the ability to generate (close to) these $15B per year in value.
Since Apple wants to keep its privacy-friendly brand, these $15B would have to come from something other than ads; and I can't think of another realistic source of revenue. But who knows, the whole "vertical integration" aspect could unlock new scenarios...
I can't find how much revenue Apple is generating from iAd, but all hints point to a fairly small number. I'm guessing that Apple keeps it around to "help" small app developers who build free apps.
And more importantly, iAd seems to focus on advertising apps themselves (like a game ad inside another game). This is a far less intrusive model than a general-purpose search engine (where you find all kinds of advertisers).
Since Apple wants to keep its privacy-friendly brand, these $15B would have to come from something other than ads; and I can't think of another realistic source of revenue. But who knows, the whole "vertical integration" aspect could unlock new scenarios...