Tell that to Japan & Sth Korea. Stable population yet increasing standard of living for its people over time. Fact is population growth is a very easy way for govts to increase growth in the short term and don't have to actually deal with the hard work of increasing productivity of the country. You are already starting to see the negative effects which aren't measured, overcrowding, land clearing etc. Keep increasing population and it will only get worse
Rome also were conquering lands and used immigration to Rome (usually of the local royalty) to keep the conquered under control, they also brought plenty of people to Rome as slaves - both not particularly relevant to modern Aus. Also Rome didn't have the level of automation we have now. Automation means that you will need less human capital over time i.e more people and less jobs....recipe for disaster long term.
