The issue would be timing. The Mirage was selected in 1960, before the Tu16s were delivered. Perhaps if they had the more powerful and fuel efficient Avon they'd be a bit more suitable for the Tu16, but I'd think they'd do the job.
Iraq and Libya got their Tu22s in 1974 or so. Assuming that the RAAF kept the Phantoms in this scenario I think they'd handle the Tu22s, but would be a bit thin on the ground. I think the Tu22 would really drive the Mirage replacement, pushing the RAAF towards an F14 or F15.
My thinking, in fact the germ of an idea I had when I ordered my multiple Airfix Lightning kits a decade ago, was that the Mirage and Bloodhound had been selected then the TU16 appeared and there was an oh crap moment.
Please be aware, I'm not trying to devalue what any of you are saying, I am just relating the AH I started developing because I wanted RAAF Lightnings and Drakens
There were flashbacks to Singapore and the Bombing of Darwin, the shortage of modern everything, including combat aircraft, memories of the Meteor in Korea when the MIG 15 appeared. In response an urgent operational requirement was launched for a very high-performance interceptor, a high-performance interceptor capable of being deployed to austere bases and a longer term requirement for the formation of an air defence command (ADC) including a reestablished flying reserve.
A realisation that more needed to be spent on defence, that a point defence interceptor was needed for vital assets, i.e. Darwin and its infrastructure, this would be the Lightning, specifically whichever surplus aircraft the RAF could spare for the RAAF. The Mirage would be skewed to the attack role and an evolved Lightning developed and introduced into service to replace the loaned examples, Australia, potentially takes the lead on the VG Lightning.
At the same time the flying reserve is reintroduced as an integrated force of fulltime, conscript and reserve personnel flying a type capable of being dispersed to austere bases in Australia's north, i.e. Draken.
It goes further, with the ADC eventually having F-14 and E-3, Mirage is optimised for strike and assigned primarily as a tactical support type, and eventually supplemented with either Jaguar or Corsair II, before being replaced with Mirage F1 then 2000.
Yes I have all the kits in my stash and am waiting for my garage redevelopment program for a cat free hobby area.