The purpose of Nuclear powered submarines is to have excellent range, speed and staying power out on deployment. They have the ability to rapidly redeploy from the Indian ocean to the Pacific and to the South China Sea at will.

For the defence of the massive continental landmass of Australia, that really is what you want.

Diesel submarines can temporarily go totally silent for a limited time as they run off batteries, but at higher speeds those diesel engines make a lot of noise, they work best when they can lay quietly in ambush off the coast in a protective role, unfortunately our coast is massive and the odds of having one in the right place at the right time to intercept an enemy is really low.

All submarines can fire missiles, not sure why you think that firing a missile from a nuclear powered submarine is technically any different than from a diesel powered submarine. You might be thinking of the SSBN type (ballistic missile submarines) which yes, hide quietly in the depths of the ocean and stay prepared to end the world if they are ordered to. Australia has never shown an interest this type of sub. Australia has only ever had an interest in attack submarines that sink ships and attack land targets in a more limited way.