How the first abortion happened is irrelevant with your idea though, it doesn't matter if the woman was young and just straight up didn't use contraception or anything like that, all that matters is every abortion after the first. It's been a pain in the ass to find stats for repeat abortions in Australia (for reasons you already know), but I was able to find a study on contraception use in relation to repeated abortions for the US and apparently women who have repeated abortions are just as likely to use contraception in general (54% for first timers), and are more likely to use a highly effective method like the pill or injectable, and those using the pill are something like 25% likely to be using it consistently. Assuming similar rates here (and I have no reason to assume they wouldn't be), that doesn't strike me as an incredibly low statistic.
Regardless, I'm not really sure what you hope to achieve if this became a thing. You want to punish women for having repeated abortions and not have to pay for it... but you're willing to pay the price of unwanted pregnancies being carried to term (lifetime subsidised medical expenses for one person is almost guaranteed to be more expensive than an abortion) or the very real possibility that the women who can't afford it will poison or disfigure themselves in order to get rid of it? There's little to no evidence of abortion being seen as a substitute for other contraception, despite the stereotype, so... what are you going for?