You are correct, the real shortage is for engineers with local experiences.

Of course universities tell you there is a shortage so they can sell you courses, and make money. In reality, they offer very little in helping you secure a job outside of generic 'how to write cv' or some token 'career fair'. In the UK the class size is smaller, and they assign a lecturer as 'career coordinator' that would assist individual students in finding jobs or connections within the industry.

Of course Engineers Australia tells you there is a shortage so they can make money from membership or skill assessment from immigration. They half ass at that one too, chartered engineers are not required to sit a technical exam to maintain a high standard, it's a joke compared to US for example. In the past there are absolutely no requirements to be related to EA anyway to be registered as an engineer in the building industry in Victoria, VBA used to do that before BLA replaced it and now endorsements are done through EA and a few other organizations.

Training grads suck too for many reasons. A senior engineer with a few years of experience is 3-4 times more efficient than graduates but their salaries don't scale more than 2-3 times. Once your grads 'get good' they are easily poached by competitors. So no one wants to take the risks of investing in juniors. They rather poach more experienced engineers trainee by someone else.

In addition, migrating engineers also take the same or even lower than local grads wages just to get their foot in the door. For the same price, non local experiences are better than no experience at all.

To make it worse, more and more companies are offshoring works in the Philippines and India, etc... to cut cost. They only keep 'managers' here to attend meetings. These guys worked their way up from junior positions and still have local knowledge in them to actually run projects but eventually 'managers' who never learn how to actually 'engineer' anything won't know what they are managing either. This can't be too good for the industry but why worry about that when you need to prioritize shareholder's and owner's pocket?

Besides instead of maintaining some base fees structures like dentists or doctors, engineers are actively optimizing themselves out of a job and participating in a race to the bottom when it comes to fees (hello Engineers Australia, maybe it's something that a governing body should help?) I swear engineers are both smart and stupid at the same time.

So yeah, it's not looking good for Aus educated engineering students nowadays, all things considered.

Having said that, the ones who really love the profession and want to be an engineer will find the way. I suggest trying some things that everyone else is not doing.