Qantas is a given, Virgin less certain. Virgin is effectively a foreign airline, so questions to be asked about why the government would be handing out money to foreign governments.
Virgin Australia might have some foreign owners but think about:
Where are the staff employed? Mostly Australia.
Routes flown? Mostly within Australia with some Pacific and a few long haul.
If profitable in the future, where are company taxes paid. To Australia.
Where is payroll tax paid? Australia.
Where is the income tax paid for most of its employees? Australia
Where are most of its subcontractors, and their staff and other business partners based and operating? Australia.
Airport owners? Mostly Australian companies (although I doubt the government is super concerned about them).
Aeronautical and security charges charges? To the Australian government.
Who benefits from competitive airfares? Australian people, and the local tourism industry in particular.
Charter business? Mostly Australian resource projects.
Velocity partners? Australian companies like Coles a few Banks, Hertz, Thrifty etc
Plus the undeniable elephant in the room that (sure VA are a bit of a mess), they are the only competitor to the Qantas group so waving through a massive monopoly on such a capital intensive highly regulated, specialised, and vital part of the transportation economy would be a massive drain on the economy.
I think owning an airline or two would be the very last resort of the current federal government, but they would certainly be open to the idea of giving some sort of assistance and relief for airlines so they at least have the time to restructure themselves and survive so that once the COVID-19 issue is over we still have a way of getting around the country.