Having obtained a Special Flight Permit (is what you're talking about) once, to move an aircraft 25 miles from a private strip to an airport, it was not an over-the-phone 5 minute job, and took about a week or two to arrange via an obliging non-CASA person who needed various information about the aircraft to be satisfied that it was in a safe condition to be operated. It wasn't any great drama, I did 90% of the work for the guy, but he had the magic ticket to write it up. He gave us a seven day window to move the aircraft which was plenty.
An over-the-phone or online to get such a permit within an hour would certainly be a good thing, but someone has to sign their name to it in the end, and if it goes to schnitzel, they are on the chopping block.
I can go to Vicroads and just buy a permit to drive my unroadworthy car all over town for repairs for 28 days, or a one off trip to move it. No questions asked.