Yes, this would defeat traffic analysis, but it only works if everyone is using the same shared channel, or if each user maintains a channel with every other user they might ever wish to communicate with. Every user must also check each packet to see if it is encrypted with their public key (requiring an extensive PKI) and is a valid message for them, which is expensive. The bandwidth required is also enormous for anything other than a very limited number of participants.

Sure, Tor achieves some of these goals, and if everyone used Tor all of the time then it would make the NSAs job much more difficult, but it isn't ever going to happen, for obvious operational and practical reasons.