When my long-term cancer patient landed in a different public hospital with unexpected bleeding complications, it soon became apparent that he was at the end of life. There were no beds in that hospital and the patient was too unwell to transfer. He died in a cubicle many hours later. The physician called me to express his regret but I reassured him I would have been in the same situation, for all that week, we had been “bed-blocked”, a term that has become part of the lexicon of medicine.

That month I had been an attending physician caring for patients with heart failure, cellulitis, falls, fractures, confusion and dementia. A few things united these men and women – they were all frail and elderly and needed a long time to improve from seemingly minor setbacks. Nursing home residents were discharged, but this still left several patients who needed slow rehabilitation and a period of confidence-building before returning home, in accordance with their wishes. A combination of an ageing population suffering from multiple comorbidities kept hospital rehabilitation beds in high demand, and it was common for otherwise stable patients to wait up to a week for such a bed. It wasn’t a judicious use of resources but there was little to change at an individual clinician level.

The plight of my deceased patient stays on my mind, and in the next few months, I wonder what I can do to make room on the ward for patients like him. Just then, a keen medical student points out that three patients awaiting rehabilitation are privately insured. “They can go to private rehab”, he suggests.

“That’s a good idea, let’s refer them”, I say, deciding to hold my judgement.

The first patient, 85, has severe arthritis. She called an ambulance when she couldn’t get off the floor. In emergency, she explained that she had top-cover private health insurance but was in too much pain to move. Five days later, she is distinctly better, but still some way off being independent. Bored of reading old magazines, she brightens at the idea of using her private health cover to access private rehabilitation. It takes two days for an assessor to approve our request. However, our sigh of relief is quickly replaced with dismay when the patient says she can’t pay the $500 excess. In her exact words, “I pay so much money for my private health cover that I can’t afford any more.” It takes a week to find her a public bed.

The second patient is 80. He is overweight, diabetic and mildly cognitively impaired due to a series of small strokes. Recently, he has been stumbling and his only slightly younger wife is exhausted from caregiving. Afraid she would hurt her back trying to heave him up, she finally brought him in when he stopped walking. They want to continue to live together in their own home, for which her minimum condition is being able walk to the bathroom. He hasn’t had a night of proper sleep and longs for a quieter space with better internet. Almost childlike in his eagerness, he tells me has top-cover health insurance and would love to go to a private rehabilitation facility.

The first assessor rejects him because “at this stage”, he requires maximal assistance. “I thought that was the point of rehab”, my intern puzzles. Two days later, a second assessor from a different facility turns him down too, bemoaning his “high level” needs.

The final assessor rejects him too. A footnote to say we should feel free to try again once the patient is walking leaves me feeling frustrated but also resigned.

The third patient is a well-presented, educated and completely bored 84-year-old who is prone to bluntness. She has also been in hospital for over a week and her fractured arm needs rehabilitation. She has spoken daily about having private health insurance but when the time comes to use it, she says, “The public hospital is convenient and just as good, so why bother?”

To my gentle hint that her decision may have an impact on the uninsured, she retorts, “That’s not my problem, dear. I’ve paid my taxes.”

Whether it’s patients not being able to afford the excess, being denied admission, being inadequately covered, or simply choosing to not use their private health cover, there are clearly many reasons why increasing numbers of insured patients are ending up in the public health system. Which is why I was confused to receive a form letter from the minister of health admonishing public hospital doctors who are continuing to “actively encourage patients to use their private health insurance to boost hospital revenue”. In fact, I wanted to protest, I am doing just the opposite, encouraging privately insured patients to use their private health insurance whenever and wherever it is possible and appropriate. It’s just that they don’t find it all that cost-effective to do so.

I am not a health economist, a politician or a hospital executive who knows all the nuances of private health insurance. I also support the idea of private health insurance and believe that well-governed and justly-administered, it can achieve many of the things it aspires to. But as a frontline clinician whose (only) allegiance is to the public hospital system, I feel I have a duty to reflect on the reality that I come across.

Many patients are led astray by the promise of private health insurance, with the much-derided “junk policies” only a part of the problem. Most of my patients are elderly and have high levels of cover. These patients, or sometimes their family, pay thousands of dollars annually for the privilege, sometimes depriving themselves of other necessities in the process.

“Peace of mind” is variously interpreted by patients as having free choice of doctor, a private room and better care – unsurprisingly the key advertised messages. The choice of a doctor is possible with elective admissions but when a patient presents with urgent needs (as most elderly do), the treating doctor is the one on the roster, especially in major private hospitals.

Private insurance does not guarantee a private room and as for the claim of better care, it is not borne out by evidence. Indeed, the worry is that care across the entire healthcare continuum is becoming increasingly fragmented. A recent study of private and public hospitals concluded that when patients stay in hospital for more than one night (as almost all elderly patients do), one in four patients incurs a complication. It turns out that good healthcare involves more than choosing your own specialist or having a private room.

Private insurance is useful in instances of elective surgery, dental care, and mental illness. These are services that the public sector groans to provide. In these instances, private health cover can improve quality of life, and for the mentally ill it can even be the difference between life and death. But all this hinges on the premise that a patient has read and understood the fine print. Major exclusions (such as for pregnancy, dialysis and joint replacements), reduced benefits and hefty out-of-pocket charges, for example for inpatient investigations, catch many patients by surprise, especially those who imagine that “fully covered” means what it says. For these hapless patients, the benefit of private health insurance proves to be a mirage as they return to join the queue for public hospital care.

With our small bank of privately insured patients who are not going anywhere fast, the medical student is astonished to hear that the government subsidises the private health insurance industry by nearly $7 billion dollars. She laments that she can’t even begin to untangle the issue but I reassure her it’s not only her, a solution seems to be out of the reach of even the best minds.

The past year has seen a 30% rise in the rate of complaints about private health insurance. Casting blame on the public health system for the shortcomings of private insurance seems to me to be a false and hasty conclusion. The time would be better spent on making the private health insurance industry more transparent, fair and accountable to the people who entrust their lives to it.

• Ranjana Srivastava is a Guardian Australia columnist and oncologist