Your proposal is also unworkable. Should companies not be required to hand over corporate records, because those might implicate them in a crime? Should a murder suspect be allowed to deny police access to his shed, where the murder weapon might be hiding? A bedrock principle of law is that “the law is entitled to every man’s evidence.” The whole point of warrants is to reconcile that principle with private property—to create a structured way for police to access private property to get access to evidence. Your proposal isn’t a “check” or “balance”—it obliterates that principle. It allows wrongdoers to hide evidence of their crimes even against a valid warrant.