Should search strings and form data in search engines and internet be End to End Encrypted ? #privacy

If we talk of privacy, then search string encryption plays a vital role too.  When other essential information on internet is encrypted then why search strings have not been encrypted. I suggest a local client-side encryption model to be implemented in any search engine, or even in essential forms we use over the internet. Lot of personal data goes into cookies which can be read by other software’s. Once the search strings are encrypted inter software -information sharing- shall be made quite minimal. And at the same time, it provides for privacy over the concerns that the search string is visible in the URL. How the URL visibility can affect us? Well, the URL goes to several routers before it finds it target destination making our personal choices in exposure to several privacy concerns.   Two-way encryption should be used. Private and Public keys should be kept different for all client applications. How it can help is routers too get a lot of data and hackers are more susceptible to know personal choices, which belong to an individual. Further, the search engines store the search history once it is encrypted, it should be decrypted only on local machines to view history logs by that software client application.