The right to privacy is not listed in the constitution.
The right to privacy exists nonetheless.
The right to privacy was not hidden for centuries. The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated... Indeed the fourth admendment declares your right to privacy as it concerns to your papers, person, effects, and home. Perhaps you are ready to grant unfeathered access to your private papers and home, but I am not quite ready to give up my right to privacy.
You are right that rights are granted by God and government exists to protect those rights. However the argument advanced in Roe Vs. Wade did not deal with that question. It dealt with the question of is there a constitutional right of privacy that makes moot any State law on the issue of abortion.
Also the right against unreasonable searches and seizures has nothing to do with the right of privacy. It has to do with the right of citizens to due process. It also acknowleges that government in excercising its power is subject to lawful restraints. If it did have to do with a right to privacy it could be argued that any search or seizure violates the right to privacy. Since you can not gather evidence against a person without violating their privacy.
The government can not search your premises or persons without following legal procedures. But provided those procedures are followed a right to privacy will not prevent them from learning about every aspect of your life and using it as they see fit.