Surely no one is giving Aus nuclear capabilities just subs that run on nuclear power , they have no offensive capability but are able to help track Chinese 'Boomers' . as they are faster and have longer endurance than Diesel boats . They used to be much noisier though -I dont know if thats still the case. I assume its mostly to keep the Aussies engagded in Five eyes and as a unsinkable aircraft carrier for the Americans in the same way they viewed the UK back in the 20th century and presumably still do.
So its not a big deal except to the many Aussies who understandably dislike nuclear anything having been used as test range by the Brits back in the 50s and 60s. Basing them in Adelaide doesn't help as the tests were done mostly in SA and Adelaide is a very liberal town, its also about three thousand miles from where any action might be. Quite what the Aussies are worried about with China and their nukes is I dont know since most of the country looks like it has already been nuked anyway and can only just support its current population in terms of water resources so no opportunity for any Chinese Lebensraum there