Strange... I wonder how that came about...
If you take America, as a similar, example.
There are quite a few, noticeable differences.
Such as driving on the right, some words in English are different, some noticeable cultural differences etc.
Ignoring obvious language differences.
I somewhat consider Germany, more similar (especially culturally) to the UK, than America.
Despite the history, of how the UK/Britain's involvement with the creation of America/Australia etc.
It's almost as though the radically different histories of USA and Australia could have had an impact on the end result!
As for USA vs Germany… (FYI, I'm an American who's lived in Europe for about 17 years.) Well, for one thing, "German" is the #1 self-identified background in USA, even above English, Irish, Italian, etc. And let me tell you,
northern Germany is clearly where many American traditions came from. But ultimately, USA is a melting pot of countless influences.
As for differences in English by country: USA tends to have retained the historical (original) forms of many words which then changed in British English (and from there went on to be exported to the younger colonies). For example, the widely known difference in "can/can't" (where American English pronounces the vowels the same, while British English pronounces them differently) is not the result of American laziness (as is usually claimed), but because that was the original form, the form used when the American colonies were established.
Add to this new words added to both vocabularies, changes that happened on one side or the other, and the influx in USA of other native English speakers (namely, Irish and Scottish, and the occasional Welsh), and it's no surprise the accents are different. But at the same time, it's important IMHO not to dwell on the 0.1% that's different, and instead to remember the 99.9% that's the same.