Building out is still a problem in Australia though, for the simple fact that the wider you spread out, the more infrastructure you need. The average Australian house is something like 2.5 times the size of the average British house, let alone European-style apartments.
Melbourne, a city of about 5.5 million people, is spread over 80kms from East-to-West and North-to-South. That's a huge area, and most of it taken up by wide roads, pavements (which people don't use because every drives by necessity) and single-story surburban housing. To compare, it's about 60kms from M25 East to M25 West around London, an area of about 10 million people.
I was trying to commute across Melbourne by public transport to get to building sites. It's okay if you wantr to go from suburb to the centre, but suburb to suburb is absolutely hopeless, sometimes with 2+ hours commutes either way. My girlfriend lived in basically the next suburb along, and it was either two buses (or a train and bus) that took nearly an hour if you missed the connection, or else a 1 hour and 20 minute walk. I got a car as soon as I could.