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.