Does that mean I can walk around anywhere in Australia with a mobile phone (or radio of some kind) with my own reflector dish and not violate EIRP limits?
Probably? Even if you were using one of these in the city, your device will automatically adjust it's gain levels anyway in order to comply with limits (to a degree). These kinds of networks are designed with "absolutely worst case" in-mind. Even if you're flying in a commercial aircraft, cell hopping every few seconds, the networks can cope with that (your device, however, may not).
In Australia, you can actually purchase active cellular repeaters, without the need for an application or a licence:
https://www.cel-fi.com. You literally just buy it and install it. The Cel-Fi products have been approved for use by all the carriers and the Australian Communications and Media Authority (ACMA), which is Australia's version of the FCC.
Back in the "old days", you used to have to apply to your cellular carrier for approval to have a repeater and they would supply it to you, provided you ticked all their boxes. Cellular coverage issues in Australia are fairly uncommon though. There are some edge cases (like my local fire brigade station) where 4G/5G doesn't penetrate enough indoors or underground. I've also seen some hard-core campers install these Cel-Fi repeaters in their 4WD/caravans for when they go "out bush" so they can have some kind of data connectivity where it's normally not possible with just a handset.