Any steam turbine plant needs a cooling system, nuclear or fossil fuel. You don't need potable water, seawater or wastewater can be used for cooling.

I would assume any steam turbine plant needs water for the steam, and that steam is eventually lost through evaporation.

the water in steam plants is a closed loop, and the heat is gathered from condensers. the water is cooled via evaporation through a cooling tower

No, they are typically closed cycle, where the steam is reused.

You just need to cool the steam with ambient air - water is better (more cooling) but hardly required.

There's this really cool invention called the bucket. It lets you recapture steam as it re-condenses.

That's one way to build them, but it's not the only way. They can be built not to need a lot of water, I assume there are some drawbacks.

And it's hardly "vast amounts", it's a small portion of the flow of a small river.

A coal plant also works better with a water source - there's no real difference here, you just need something to cool the steam at the end.

If coal can work in Australia so can nuclear.

The middle of the country has no need for large quantities of power as almost nobody lives there - almost all Australians live on the coasts near to water.

Or, to generalize even further -- the vast majority of Australians live in or around a handful of cities along the southeast coast of the country (Sydney, Melbourne, Brisbane, Adelaide, Canberra), or one city on the west coast (Perth).

A map of the country's population density may help bring this into perspective: https://i.redd.it/9mw8ttqqu0b41.jpg

Almost all largely populated areas in Australia are coastal.

No you don't. At high temperatures, you can use air cooling...