Here is the problem with that: Apple would have a public-facing online search engine. The article addresses the advantages for Apple of having Safari users use Apple's search engine, but does not mention what the strategy would be for non-Apple users. Would they make a full-fledged search engine that optimises advertising for users who are not using Apple devices?
That's not to say it's not a good idea - a lot would depend on the quality of the search that Apple would be able to provide.