If it is a switch in the UI, then that is just trusting the site. If you trust companies with what they say they do, then why not enter your query in any searc

If it is a switch in the UI, then that is just trusting the site. If you trust companies with what they say they do, then why not enter your query in any search engine that does not require a login? Afaik none of them say that they will try to apply fuzzy fingerprinting to cluster your searches into a profile.