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.
Why would Apple need to worry about non-Apple users?
Ultimately they could offer the service to them but they may find having Apple Search exclusive to their devices as a positive. It would allow them to offer many unique features such as integrating local and web results seamlessly (amongst many other ideas).
Also, and Apple knows this more than anyone, Apple users are the most capable in their ability to spend money. So although Safari users would be only 20% of the global search market, it's likely the most lucrative 20%.
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.