At least when running on Internode hardware, the traffic only runs on Telstra copper; once terminated at the exchange (on Agile/Internode DSLAM), it pushes out into Internode's backhaul/network. (It's a moot point if the backhaul is Telstra owned I guess, or significant parts of the private network is leased from Telstra...)

Still worse, as mandated by the Australian government, won't all internet traffic eventually switch over to the new government owned/controlled FTTP and wireless infrastructure of the National Broadband Network?

In our area the NBN has gone up recently, and we've received letters saying that the existing copper network will be decommissioned in a year so all landline phone users will need to get an NBN connection. If the Aus govt is baking intercept points into the NBN (not hard to imagine) then they'll be able to intercept phone traffic as well, whether they get cooperation from telcos or not.

From what I understand, the government has required the telcos to sign agreements forcing them to cooperate with the transition to NBN infrastructure.

There's nothing like that happening. They are paying Telstra and Optus a pretty good deal to migrate customers off legacy HFC and copper telephone networks though. But no forcing is happening...