Well... one reason may be that they can no longer justify quarantine. If we look at the reason why we have quarantine, it's to stop severe illness or death if the virus hits vulnerable populations. If the vaccines work as the CHO says, that risk will drop to a reasonable/acceptable level.
The Cth originally outlines that all of Australia would be vaccinated by the end of October. They've now advised the vaccination program wil start a good six weeks earlier than planned, so that should give an end date of mid September rather than the end of October. And those at the end will be low risk anyway.
So that time - mid September - fits nicely with the date they need to decide whether to extend the emergency ban on departures/arrivals. So September at this stage is looking reasonable IMO.
The way the Australian government has acted with regards to this virus in being way too conservative and taking a we'll wait and see attitude to everything has made me lose optimism on anything being eased in 2021.
BUT, I like your version more, and I'm just going to hope and pray that what you have laid out happens; and if things can be eased before September, we'll take it as a bonus