I find the vast majority of people who 'prefer an insurance based system' both have excess money and also no experience of an actual insurance based system.
I'm from the UK, currently doing a healthcare research project in the USA. I promise you, you don't want this system.
Not only are there copays every time you see a doctor (ranging from $5 to $100+), there is a monthly premium, which can easily be over $500, that's before including your family.
On top of that, there's co-insurance. So, say you have an ultrasound, it was $1000. You pay a copay for the right to see them in the first place, then also a percentage of that $1000, which can be from 5-50%.
And that is assuming you've met your deductible - usually thousands of dollars, which you yourself have to pay before insurance will pay anything. And that is on top of those monthly premiums of hundreds.
And all this before I've even gotten to prescriptions. It is your insurance company which gets to decide which medication you can take - not your doctor. Unless you also have hundreds of dollars a month to spend on them. Some medications, even with insurance, have a copay of $100. even life saving medications such as insulin.
I assure you, unless you have a current monthly surplus in your budget of a couple thousand, you don't want an insurance based system.