How did USA end up with quite a few distinct dialects and Australia end up with more or less one, given their similar colonial pasts?

Speaking Our Language by Bruce Moore, Oxford University Press 2008, explained the homogeneity of Australian English as follows—as I summarised it in History of Australian English on my Hellenisteukontos blog:

Moore puts forward the formation of an Australian English as a dialect koine in Sydney, within two generations of settlement, and then diffusing out of there rapidly. (There were no administrative barriers between provinces like in the States, hence the astonishing regional homogeneity of Australian English.) This is common sense, and reflects other koineisations (and creolisations). New Zealand has done a better job than Australians of tracking their linguistic history, and the accent data from the first generation of native born New Zealanders, available through recordings done in the 1940s, was critical to proving that contention. Their accents were not yet fully levelled, and even children growing up in the same small town had slightly different accents. It was only the second generation of native born colonists who had a local norm to peer pressure themselves into, and knock out any deviation.

In line with that, it was only after the second generation that dialect loans from Northern English and Scots into Australian English were possible. In the first generation, such words were still sensed as outliers from the emerging Southern-England based koine, and ruled out.