Australia is already building a lot of pumped storage. E.g. snowy 2 alone has 350 GWh of storage. Im skeptical of the idea that this + solar + wind costs more than nuclear + this even without free catastrophe insurance but id be curious to see your numbers.

(Obviously some form of storage would also be necessary for nuclear power which cant adjust output to match variable demand).

It is pretty cheap to build pumped storage, relatively. Pumping water uphill isnt too complicated. Until a few months ago though the cheapest "battery" was still natural gas.

Pumped storage is an unsexy 100 year old technology and it doesnt have a huge lobby doing public relations like the nuke industry so when big projects go ahead we tend not to hear about it but there are tons in the pipeline all over.