Because of the minimal money going into facilities, they tend to keep their costs low by keeping full-time staff to a minimum; casual is the most common position because there are minimal "penalties" and paid time off. That's the nature of the industry, I'm afraid, and you'll find that pretty much anywhere you try. The only people who get full-time positions are highly-experienced and highly-trained; basically, irreplacable people.
That said, casual is better than it sounds. You start off with a few rostered shifts, and the rest are call-ins. As a casual, I was earning upwards of $1100 EVERY pay, because I built a reputation as someone who almost never said no, even when they called at 6am for a 6:30am shift. That's how you get the good money. It doesn't have the benefits of full-time work like annual leave, but you can get a lot of work out of it if they get to know you'll turn up at a moment's notice.
Don't let the term "casual" put you off. I got the same spiel about "not a lot of shifts to go around/lot of people on their books/etc", but what they don't tell you is that your position on that list of "on-call workers" varies according to your reliability; the more they can rely on you, the more likely you'll be the first person called. Within my first month, I was getting 50+ hours per fortnight. That's not bad at all for a casual.
Start low, work up. That's the way to go, and the ONLY way you'll get a foot in the door.