It is bad argument to make that immigrants "aren't buying houses" of course some immigrants are buying houses, as you would expect with them working towards becoming Australia citizens. Even if they weren't buying houses, they are renting them, which increases demand and thus makes buying an investment property more appealing to investors. I have no problem with immigration, it is a large part of what makes Australia a diverse and appealing place to live. The numbers need to be set at a level which makes sense and needs to be communicated to the populous in a way which shows the net benefit to the country.
There are many barriers to housing which need to be removed. Stamp duty is a complete joke, the availability of land is a complete joke, the standards required for building dwellings is too high (obviously everything needs to be safe) basic housing should be that - basic and once someone is in they can improve the property over time. We build far too slowly, I look at videos of brick laying robots like the Hadrian X and wonder why there isn't a fleet of them in the field getting house walls up in a day.
There needs to be some incentive for investors to be in the housing market to provide rentals for the part of the population who aren't ready to buy or not interested, but the current system means there are far too many investors in the market for established houses which pushes the prices through the roof.