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The Smartraveller.gov.au web site advice for New Zealand gives some more details of why you'd want travel insurance, such as medical expenses outside New Zealand, or medical evacuation following an accident:
Australians seriously injured in accidents in New Zealand may suffer significant financial losses from loss of income or medical expenses on return to Australia. New Zealandβs Accident Compensation Act 2001 generally removes the right to sue for losses arising from personal injury sustained in accidents in New Zealand (e.g. motor vehicle or adventure sports accidents). The Act also excludes Australians from obtaining the ongoing income support provided to New Zealanders and from coverage of any medical expenses outside New Zealand. Also not covered is illness, medical evacuation following an accident, disrupted travel plans, lost deposits, assisted emergency travel home or travel for a relative to visit you. For more information visit the Accident Compensation Corporation (ACC) website.
We strongly recommend that you take out comprehensive travel insurance when travelling to New Zealand. We also strongly recommend you obtain separate personal accident or income protection insurance policies that will cover lost income or medical expenses in Australia arising from accidents in New Zealand. You should understand what activities and circumstances are covered by your insurance policy.
Ensure the travel insurance covers any overseas medical costs, including medical evacuation, before you depart. Confirm that your insurance covers you for the whole time you'll be away and check what circumstances and activities (including adventure sports / activities) are not included in your policy. Remember, regardless of how healthy and fit you are, if you can't afford travel insurance, you can't afford to travel. The Australian Government will not pay for a traveller's medical expenses overseas or medical evacuation costs.
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New Zealand and Australia are signatories to a reciprocal health care agreement. The agreement provides Australians with access to government medical facilities and care but does not provide for ongoing treatment of existing health conditions. In addition, the agreement does not cover additional accommodation costs, flights for family members or medical repatriation to Australia. The Reciprocal Health Care Agreement does not replace the need for travel insurance. See Medicare Australia's website for more information.
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In addition to unexpected expenses if you suffer an injury in the other country, you might have a health problem in your own country preventing you from travelling, and travel insurance will cover the cost of your jouney which you never had.
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Reciprocal agreements will normally cover the actual medical care but there can be other expenses involved with getting sick/injured while abroad which won't be covered. Accomodation costs can be significant if the emergency delays your travel home. If you are hospitalised on a longer-term basis then the cost of transport home in the injured state can be very high (even a simple broken leg can result in having to pay for multiple seats).
Another consideration, not so relavent to the AU->NZ case but very relavent to say AU->UK is the travel itself. If you have a medical emergency while travelling then you could end up in a hospital at any layover location or even at any location along the flightpath.