The battery you mention will be for those who have a FTTP connection (fibre to your house). When the NBN was first starting to be rolled out, there was some issues raised by the then opposition (LNP) about loss of connection in a blackout so a back-up battery solution was included in the fibre box on the wall. My understanding is it was to power the UNI-V ports (phone) and not any of the UNI-D (internet) ports in the box.
If you have FTTN, Sat, HFC (Cable), Fixed Wireless as most of the rollout is now, then the battery is not part of the install, as far as I know.
At the time battery program was introduced it was covered in the press quite extensively. Much of the coverage was negative for various reasons. Originally the battery was included, later it was optional. But the cost of replacement was the customers responsibility.
This is just like the UPS power supply I and many others have now connected to their computers at home for the same reason. It allows my computers to keep running when the power goes out and this allows me to save my work and shutdown normally rather than have it just die on me. I have to replace the battery every 3-5 years ($100 per battery).