A fair point, but the controlling "document" isn't 200 years old. In fact, it's 46 years old[0] and is called the Third-Party Doctrine:
"The third-party doctrine is a United States legal doctrine that holds that people who voluntarily give information to third parties—such as banks, phone companies, internet service providers (ISPs), and e-mail servers—have "no reasonable expectation of privacy" in that information. A lack of privacy protection allows the United States government to obtain information from third parties without a legal warrant and without otherwise complying with the Fourth Amendment prohibition against search and seizure without probable cause and a judicial search warrant"
The tl;dr is that if you voluntarily give a third party (not the government and not you) information (e.g., web search requests), that information is not protected under the 4th Amendment.
As such, even though the police got a warrant, it wasn't necessary for them to do so unless Google balked at providing the information.