Bluetongue, I've used both systems extensively. You say you might as well take your chances with the public system- well the Australian public system is head and shoulders above the nhs in terms of wait times in my experience. I have recently waited over a year for a pediatric heart appt here, we waited about 3-4 weeks tops for the same in oz when it was non urgent. In addition, yes there can be a "gap" if you take out the lower types of insurance, but there are ways to minimise it, and you can always use the public system. There are also limits on what a family has to pay each year in terms of Gap. (somewhere around $1500 from memory.)
Let's take an example of why I prefer the Australian system.
My sister was diagnosed with melanoma in the UK. It went like this:
She rings GP to make appt because of black mole on thigh. Two week wait for GP appointment as it's not an emergency. Gp says she thinks it's nothing, go home. Sister is worried as she has used sunbeds and the mole is really black so begs GP for an nhs referral. GP agrees after sister almost in tears.
Wait for consultant appointment is seven weeks because she's not fast tracked as gp doesn't think it's likely to be cancer. When she gets there the consultant looks and says probably nothing, watch and wait. Sister begs so they agree to remove it instead. Schedules her in for minor surgery clinic. Appointment comes in- for two weeks later. (at this point it's 11 weeks since she called her gp).
After the removal she waits four weeks for her biopsy results. She gets them in a letter that tells her that she has melanoma and needs further surgery as the margins weren't clear.
She has to google it because she doesn't know exactly what melanoma is, and only discovers that she has a very aggressive cancer via google. To be fair, at this point the nhs speeds up and she has pretty extensive surgery only 7-8 days later and starts treatment.
By contrast, I was living in Australia. Found a black mole on my shin that looked dodgy. Called my GP and was offered a choice of same day appointments. The Gap (what I had to pay) was $25ish. (note, if I was on benefits or elderly I wouldn't have to pay this) Saw him that day and he was worried it was melanoma because it was black. Put me on the fast track to (public) dermatology and I was seen four days later. At the clinic they removed the mole immediately and another one they thought also looked dodgy. The next morning they called with my biopsy results, which thankfully showed it wasn't melanoma. The whole thing cost me $25ish.
I have numerous other examples of similar things in my family. So whilst I had to pay something, I'd rather pay and be seen quickly. Had I gone private it would have cost me more, (the gap may have been $100-200 maybe for that)
Incidentally, after her treatment my sister was offered one follow up check six months later. After that nothing. This is outrageous given the risk of further melanomas and recurrence. In Australia she'd be followed up regularly for years, probably forever. She was told they don't have budget for any more.