Imagine some kind of worldwide system, without a central server and dedicated administrator, distributed among a large, constantly changing conglomeration of servers that store and forward messages to one another.
In your dreams!
Because if people did, anti-piracy companies would start paying attention to it. Therfore making it way more expensive to run Usenet servers and expose users to legal risk.
It's success depends on its relative obscurity.
You have to provide a credit card to use Usenet (unless you use bitcoins). Making it easy to be targeted.
Torrents "done properly" can be completely anonymous for everyone involved and still free.
So I don't agree that the problem was completely solved by Usenet. Despite being a happy Usenet + NZBmatrix user (oops broke the rule :p).
Which does nothing but say you accessed the server- not what for. Furthermore, the better providers don't keep logs.