Primary position

What does the Australian law state about riding in primary position?

Joni, you want to make a wider point about cycle training. Taking the 'primary position' is merely one technique that gets taught within this. It is also, all too often, misunderstood as constituting 'vehicular cycling', which is nonsense--vehicular cycling includes lots of techniques and is actually, in summary, simply 'riding a bicycle in accordance with the rules for drivers of vehicles'.

Ed is spot on in asking about the state of the law--whether or not riders are allowed to observe the rules for drivers of vehicles depends on whether this is legally permitted in the first place. There are plenty of places in the world in which the rules for drivers and riders differ quite considerably (usually to the detriment of the rider; at its heart this is a battle about rights).

As examples, in the US, taking the lane is expressly permitted (by federal and not state-specific legislation, I believe, although I may be wrong) in lanes up to 14' in width, and in Britain the legislation is typically silent about it, meaning that it is permitted. I have no idea what the law says on that in Australia, and a quick web search doesn't give answers.

Once you've established this (and seen what can lawfully be advocated), it is worth embedding taking the primary position in its proper context. As I said above, too many people wrongly believe that it is somehow a standalone thing (loads of daft blog posts about that). Instead, as I said above, it is one of the techniques in vehicular cycling, which in turn is part of effective cycling (and the latter also includes things such as being able to fix (some of the likely problems with) your own bike.

The main reason for what you're probably seeing in Melbourne at the moment is the general ignorance of the basic skillset involved in cycling--knowing how to lock, how to clean, how to repair, and last but not least how to ride a bike, to name just a few things. Occupations whose skills are not widely known, practised, or accepted in a society will enjoy a lower social standing, e.g. people think that riding a bike is very easy and that for the most part it's poor (or foolhardy) people who do it. Embedding these skills in a society is the key to changing things. For instance, decades ago swimming wasn't valued, and people thought that those who went into the water deliberately weren't quite right in the head. Today it's generally acknowledged as an essential skill.

Obviously, Australia has a bit of a mountain to climb in this regard. It is worth noting that some of the most visible people connected with cycling, e.g. racing cyclists, whom some people would expect to have all the skills, often have a very one-sided and limited skillset, e.g. in relation to riding in mixed traffic--they're great at riding in bunches of racers at very close quarters, because there they know that certain reliable social standards apply and this makes others' behaviour predictable to them. Where such standards don't exist and interaction of different modes is ill-defined, they often have considerable problems, and some humble commuter who could never win a race if they tried might have much better skills.

skydancer may know whether there are any budding training providers in Australia.

I know none of this widening of the scope necessarily makes it easier--it's a lot of hard work! Good luck.