I believe that unless you agree to it, that you would not be liable to contribute to any private health care payments. In fact when I looked into private health care (2007) and took some out, I asked the ex if she would be willing to pay part of the difference between the cost for myself and my wife and the cost to include my son (the ex was the primary carer then) and I would then have him added thus allowing benefits (actually I would still have got the cover if the ex disagreed). Anyway as it turned out the policy included children at no extra cost at all. Certainly the cost to add a child would not be 50% of the cost. If I recall correctly of all the funds I checked only one, the defence force's scheme, actually had a different charge for including children.
I also believe that single parents (may only be single mothers) can get reductions for private healthcare, perhaps based upon the ex's line of thinking, she should be paying you for this reduction, if she could claim as a single parent.
I believe that you are also correct in determining that such amounts are part of what CS is for, the cost of a child was based upon research that equated to something around $500,000 for their first 21 years for the average child and therefore includes most normal circumstances such as schooling, medical costs and costs for extra-curricular activities.
The ex, could try (well actually should not be able) for a change of assessment however I believe this is not a special situation under which a reason 2 change of assessment should be made (note the use of should as the CSA have been known to make some very extraordinary decisions when it comes to what is considered as special circumstances, which all appear to fit in the collect more at any cost model that appears to be used very frequently by the CSA). I don't believe that this could be considered as training or education and thus would not come in as a reason 3 change of assessment, although it could be considered caring, but then it is obviously not the level of care expected (that is unless such cover was previously provided). All the other 8 reasons are even further away from including this.
It would appear that this is an attempt to exploit the child or children for monetary gain, which should, in my opinion, constitute an abuse of the child or children.
It could be a different matter if the matter were taken to court, however I suspect that an attempt to do so, would likely fail. Perhaps the SRL's would like to comment on this aspect.
Note by children I mean biological children, not just any children. I'm sure the policies word this better than I have.