If a country installs Huawei wireless networks, it would be impossible to prevent China from spying on them. The same is surely true with with US wireless networks: it would be impossible to keep the US from spying on them.

The Australian government may not mind if the US spies on Australians. Indeed, reports are that the US government spies on Australians and gives the data to the Australian government so that it can bypass the legal protections of Australian law (and vice versa). Still it seems foolish to build in vulnerability like that.