Public transport airport transfers in Melbourne, Brisbane, Perth, and Adelaide:
Not 'there' yet, but getting better.
The big complaint is payment. Apart from Adelaide (surprisingly), you can't just tap and go with a credit card.
Even if the airport shuttle itself sports shiny new payment facilities, if you transfer to other public transport you are faced with outdated systems.
This often means buying an expensive city-locked transit card, or paying with cash(!), as in Perth.
Still, it's far cheaper than taxis and rideshare.
To be fair, things are moving. Brisbane and Perth are slowly phasing in credit card payment. Melbourne has app-based payment* even though its airport buses are a separate, private system altogether.
* (Card readers in Melbourne have trouble with both apps and cards, but there's few inspectors, so... Also, Japan phones (e.g. my spouse's) have wallet apps locked out of international payment systems.
