Churchill certainly made mistakes which cost Australian lives (e.g. Gallipoli) but you contradict yourself, though I think unwittingly....
Churchill's strategic imperatives did not include consideration of Australia. His disasters in Greece, Crete (against the advice of his military), and Singapore cost 20,000 Australian casualties killed or captured.
His defining strategy was the preservation of the Empire without compromise.
Therefor we Australians can be grateful for the heritage but we owe them nothing....
Chris
Preservation of the Empire included protection of the Dominions, & fighting for Singapore (the right thing to do, but badly executed) was forward defence of Australia.
I think Churchill didn't see a divide between Australia (& the other Dominions) & the UK. He took it for granted that they would fight for each other. He didn't see himself as using Australians to fight for the UK, or vice-versa, but using soldiers of the Empire to fight for the Empire. The British sailors who died in the Java Sea, for example, were fighting for Australia as well as the NEI.