RE: A new citizen comes bearing her parents' gift: could open borders enrich us all?
You are a classic case of 'all the jelly beans are blue". I.E. You stick your hand in a jar of mixed jelly beans, pull out a blue one and declare to all present that all the jelly beans are blue, despite the evidence in your face.
Some immigrants are great people and contribute positively to Australian society. But some ARE NOT!
Two facts remain and cannot be disputed other than by individuals driven by ideology rather than rationality.
1) All potential immigrants cannot come to Australia even if they are like your immigrant friend. We do not have adequate fresh water at all times to sustain a significantly larger population. Nor enough fertile soils suitable for food production.
2) As long as immigration is as high as it currently is, immigrants will not be screened properly by the immigration authorities because they lack the required resources to cope with the numbers. As a result the criminals or criminally inclined will be let into Australia along with the great people like your friend.
Both require immigration to fall to far more sustainable levels.