The fact that what comes out of the decryption process is a message and not gibberish means that it was encrypted with my private key. Since only I possess my private key, I must be the source of the message. By encrypting first with my private key and then with your public key, I can send you a message that is both secure and verifiable. Only you can read it, and only I could have sent it. Related technologies will provide additional elements of privacy.
Protocols exist to make communications untracable as well as secure.
Combine all of these and we are in a world of strong privacy. That is a small part of the real issue. Computers and computer networks make possible a level of privacy stronger than we have ever had. In a world of strong privacy, a large part of human activity will be unobservable to anyone save the participants. What cannot be observed cannot be taxed or regulated.