As long as one single entity tries to maintain at least a 60% share of the market then there is definitely room for competition. QF holds a monopolistic advantage, which does stifle competition, it is being eroded slowly, but surely. As many domestic carriers can exist as you want, if the others are not colluding to destroy new entrants and share the market. This is the same issue throughout a lot of the Australian economy, telco industry, mail industry, etc, all so called free markets but significantly controlled by the ex government incumbents. Australia has very weak anti competition laws and anti monopoly laws, so the large companies basically do what they want and drag it out in court with their vast resources. Then if you dare touch actually get anywhere with these ex gov companies they pull out the old 'but we're Australian card' and garner support, when in fact they are just another public company now.
And if you count QF and J* as separate companies you are delusional. Its like saying there's more than 3 or so players in the insurance market, eg YouI is a branch of AAMI for more discerning customers (who like to pay more for the same thing) and so on.