The sensiblish way to implement this would be to make each packet contain a cryptographically strong checksum of this and all previous packets in the TCP connec

The sensiblish way to implement this would be to make each packet contain a cryptographically strong checksum of this and all previous packets in the TCP connection. It could be done better by including the next packet, too (which would require sending an empty TCP segment when a checksum needed to be sent before the content was known), and even better by reinventing TLS, and even better than that by simply using TLS.