This is what happened with the USSR & the USA in the 1960s in that a percieved first strike advantage was negated by a rapid & overwhelming predicted response. This cemented the Cold War and despite the economic implosion of the USSR due to the expense of the arms race & the break oup of its satellite states, Russia still has the number of nukes & the means to deliver them to deter a US first strike.
Add an emerging China into the mix and life for the US Hawks .
If history id doomed to repeat itself, the big question is whether the USA or China will economically implode first in their desperate and costly strategies to keep ahead in this second Nuke Arms Race?
A warship here or there whether it be a Chinese one close to our territorial waters or an Aussie warship close to Chinese territorial waters is simply political window-dressing IMO.
The real deal is China's Nuking-up to push back the USA from the China Sea. IMO the compromise will be faced by China when its nuked up to have a Nuke presence close to the US mainland & then there'll be a tit for tat deal: The US withdraws from the South China Sea & China withdraws from the Pacific & Atlantic .
At present the Atlantic and environs is over populated with Nukes by the USA, UK, France & Russia.