If you split a control into two, more granular, controls, the default should be whatever I, the user, set the original control to be.

Having the default be a more privacy protecting setting is better than the default being the best for ad tracking, but really it should be what I wanted.

You've just identified that the Google Search operator is not Google's primary user, it is the advertisers that Google's entire existence is geared of appease, the search function is just how they collect our desires to feed back to their real users, the advertising industry.