As lifetime holders of private health insurance, we didn't give any thought to the medical bills that would be associated with the procedure. We have top hospital cover so assumed we would be covered. We weren't.

When the doctor's rooms rang a few days after the procedure to inform my husband our health fund had declined to pay the bill, we both thought there had been an error. There hadn't.

As it turned out, there was a single non-cosmetic hospital procedure that wasn't covered by our insurance, for which we pay upwards of $3000 a year, and that procedure was the one my husband required.

We began the year by forking out almost $3000 for something we hadn't budgeted for, which is precisely the reason we have insurance.

Our mistake was an obvious one: we should have called our insurer before he had the procedure. If we had known it wasn't covered, we could have put the procedure off until we had boosted our cover to include the extraction of wisdom teeth or used the public hospital system.

In our defence, we were due to welcome a new baby into our family a month later and keen to have the situation dealt with as quickly as possible.

Ian McAuley, a research fellow at the Centre for Policy Development, has researched the private health insurance industry extensively and says this situation is far from unique.

"We call these 'unexpected gaps' and various Australian Competition and Consumer Commission reports have looked into it," McAuley says.

The point at which many Australians realise their insurance is inadequate is when they are diagnosed with a problem and make an inquiry or claim.

"Picture the person who has contributed to insurance for a long time, hasn't ever drawn on it and then hits an age when something happens and for the first time they confront the situation where they have a need ??? and their insurer won't pay out," he says.

This predicament inevitably prompts consumers to examine whether their private health insurance is worth it.

Given premiums having risen steadily, it's unsurprising that many consumers are lowering their coverage or opting out altogether.

But, according to the ombudsman's 2015 annual report, this creates a vicious cycle: "Many [complaints] are related to decisions made by health insurers in attempting to keep health insurance premiums lower by making changes to health insurance policies; and by consumers choosing health insurance policies with restrictions and exclusions, in return for paying a lower premium."

The proliferation of "junk" private healthy policies, which Australian Medical Association president Michael Gannon describes as "not being worth the paper they're written on", means policy holders are being short-changed and the burden on the public health system isn't being relieved, which is the main reason consumers are given a tax incentive to take up private health insurance.

Junk policies are those that exclude common procedures such as hip and knee replacements, and provide so little choice of providers that policy holders inevitably end up using the public system.

It brings the efficacy of subsidising private health insurance into question.

Anyone earning more than $90,000 a year in Australia who doesn't have health insurance will pay extra tax, in the form of the Medicare Levy Surcharge. There is also a Lifetime Health Cover loading that goes up by 2 percentage points every year a person delays taking out private health insurance after the age of 31 and until they're 65.

Regardless of their health needs, McAuley says it is an individual's personal tax position that determines, in financial terms, if they are better off paying for private health insurance or wearing the tax penalties for not having it.

"People are getting annoyed," he says. "It's heightened somewhat because incomes aren't rising and household budgets are being squeezed. When people feel pressure - they examine what they can do without."

McAuley says in many cases private health insurance simply doesn't deliver.

"In addition to the unexpected gaps in coverage, people are buying a heap of insurance they don't need and never use," McAuley says.

"One of the big areas of unnecessary coverage is ancillary insurance. Insurers make a lot of profit from coverage for things like ophthalmology and dental where the 'so-called' insurance products only ever cover a small amount of the cost."

For example, McAuley says a policy that pays for dental fees up to $1000 is more accurately described as "a little help paying the bills".

"It's a complete violation of insurance because you might be able to cover those initial bills but it's where the cost racks up beyond that when you actually need the insurance to kick in," McAuley says. "This is a total reversal of the purpose of insurance."

It is unsurprising then that complaints are on the rise.

The private health insurance ombudsman reports that it received 4416 complaints from consumers in the 2015-16 financial year. Between 2006-07 and 2010-11, complaints rose, on average, by slightly more than 30 per cent each year and between 2011-12 and 2015-16 that increased to 47.4 per cent.

McAuley says most Australians are better off without private health insurance. The exceptions are high-income earners, and many people managing chronic illness, aged over 55, and women planning to become pregnant.

Georgina Dent is a journalist, editor and TV commentator with a focus on women's empowerment and gender equality.