What if indeed? Turns out there are. There is a growing desire for a simple search engine that only does the job of searching, not profiling you for various marketeers. A good example is duckduckgo.com. The searches are simple, accurate, no nonsense, and there's a firefox plugin. This is from their "about us" pages:

At other search engines, when you do a search and then click on a link, your search terms are sent to that site you clicked on (in the HTTP referrer header). We call this sharing of personal information "search leakage." For example, when you search for something private, you are sharing that private search not only with your search engine, but also with all the sites that you clicked on (for that search). In addition, when you visit any site, your computer automatically sends information about it to that site (including your User agent and IP address). This information can often be used to identify you directly. So when you do that private search, not only can those other sites know your search terms, but they can also know that you searched it. It is this combination of available information about you that raises privacy concerns. DuckDuckGo prevents search leakage by default. Instead, when you click on a link on our site, we route (redirect) that request in such a way so that it does not send your search terms to other sites. The other sites will still know that you visited them, but they will not know what search you entered beforehand.

Not bad. Indeed I find it spooky that if I go to search for a faucet one day, I suddenly notice that all the online advertisements on pages I visit are showing me ads for the same faucet all the time. No longer. Thank you Duck Duck Go!