Serious illness can mean a total disruption in family life. It may mean an income earner is unable to produce income (at least for a time) with corresponding financial pressure.

trauma insurance is a living cover.

 It pays a tax-free lump sum to the insured for up to 45 health conditions that are specified in the policy wording. There is some variation in the conditions depending on the insurer, but the main ones are common to all insurers. 85% of all claims are for cancer, heart attack and stroke.
It may mean that treatment not paid for by the public health system, could be beneficial.

For example: There's a cancer drug called Keytruda. It’s very effective for some cancers. It’s very expensive and it’s not paid for by the Health System for all cancers. (it recently became funded for some cancers such as advanced melanoma’s, but not metastatic bowel cancer for which it is also effective). Trauma insurance can be used to pay for such medications.

Some people use the money from a Trauma Insurance claim to pay down debt and make life more bearable, in that way. Reduce the financial pressure.
In short it can provide an essential buffer when things go wrong.