I suspect its to do with optics as well as logistics. From a political pov, its pretty bad optics to take them to say Dubai then leave them there with last minute costs for everything. I can see the news headlines already.
Agreed that the optics don't look good and for a political party that counts on the minority vote it may very well be even politically expedient for them to do so. And I suppose too, one could argue who cares, it's not a lot of money and it's the government's money anyway. After all, I suspect if any of us pored over the budget of the Commonwealth we would find spending we would personally object to, whereas other items we would support.
But I do sincerely wonder if this Cyprus plan that they have planned will work out as they hoped, or whether once the dust has settled they realize they could have done more good simply facilitating travel to these safe countries instead. A Qantas 787 can seat somewhere around 236 passengers give or take. Now I don't know how many Aussies (and Kiwis for that matter) are in Lebanon and require repatriation. But I wouldn't be surprised if it is an order of magnitude larger than the seating capacity of one of these jets.
And as much as the optics of an Aussie being stuck in Dubai looks, it will be far worse if a single Aussie is injured (or worse) dies in Lebanon because the government spent all their resources focusing on the long haul travel of the mission but failed to spend adequate resources securing their safe passage to these third countries. I've said it before and I'll say it again, the long haul part of the travel is really the easy bit, once you are in a city like Dubai or even Larnaca. The tough bit is actually moving those couple of hundred or thousand kilometres to safety and that is something the Commonwealth and frankly other nations supporting rescue efforts should focus on. Every single Aussie needs to be able to leave Lebanon safely. That should be the mission. Anything else is icing on the cake.
From Qantas' PoV if they accept this, where do they send the plane next? SIN? SYD? PER? It'd be easier to restart their schedule from the normal Aussie ports than run another useless deadhead flight so might as well take them home.
Why is there a need for Qantas or any airline for that matter to provide support if DFAT can organize travel to these caught out travellers to a nearby safe zone like Cyprus or Dubai. Certainly, once they get to these locations, there will be other airlines far more equipped to help repatriate Aussies than Qantas ever would. Take Dubai as an example, there are tons of flights Emirates operates not just between Dubai and Australia but also New Zealand for that matter.
As for the final point, if they want to head back then that's on them now. Repatriation flights aren't continuously run.
They may not be continuously run but from prior experiences (i.e. COVID repatriation flights) I highly doubt this will be all of the flights we'll see organized by DFAT. Now certainly what happened to Aussies caught out during COVID is quite a bit different from what is going on here in Lebanon. But one could argue that it is politically expedient for the government to provide the same level of support for stranded Aussies.