What makes governments any more susceptible to corruption than a private organization?
I’m not actually talking about governments having absolute control. That’s a pretty extreme scenario to jump to from from the question of if it’s better for a private company or a government to control search.
Right now we think Google is misusing that data. We can’t even get information on it without a leak. The government has a flawed FOIA system but Google has nothing of the sort. The only way we’re protected from corruption at Google (and historically speaking several other large private organization) is when the government steps in and stops them.
Governments often handle corruption poorly but I can rattle of many cases where governments managed to reduce corruption on their own (ie without requiring a revolution). In many cases the source of that corruption was large private organizations.