I'm a fan you know, so i know what is supposed to happen if Australia wins. What i don't know is the reasons why they're not hosting it (more than just not being in Europe, seems a weak excuse imo)
I do think costs factor into it quite significantly. If you imagine each country participating might be wanting to send 10 people - an average of 5 for the stage, some commentators, composers, delegation etc. - then that already brings the total to 430 people, and if we say that maybe 70 others from the EBU, planning committees, press etc. would be involved, that brings it to 500 people travelling to the other side of the country. For each of those, even travelling economy, a $100 dollar return trip would probably become more like a $1500 return trip - which, multiplied by 500 people, already means $700,000 that nobody will want to pay for. Add onto that the costs of moving around any props that would be wanted, the fact that Australian hotels are notoriously expensive, our crappy public transport, and you've got some more issues. And then, as you've said earlier, we'd need to start early in the morning if we wanted Europe to get the broadcast at the usual time. It might not
sound too bad, but it means you've got to be moving around thousands of performers, press and viewers before public transport has even started up for the morning, making the singers perform as early as 5AM (or 1-2AM if you consider rehearsals)... it wouldn't be easy.
It's not impossible, and I'd love to see it happen so that I could go to Eurovision without having to fly over to the other side of the world, but logistically I think all the organisers would rather avoid it.