In CA, my doctor can refer me to get a Cologuard. But it's private pay, and they want payment up front since isurance companies don't restrict doctor's ability, only reimbursement.

So they may not be willing (even though they are able) perform procedure/test if they aren't confident they'll get paid.

You are just ignoring their intended meaning. Boring.

Is the intended meaning that health insurance should pay for anything and everything? Even systems where the government pays directly like the UK have parameters under which the government will pay for a procedure or medicine.

Not at all. Patients are free to pay out of pocket for procedures not covered by insurance. An extra colonoscopy (one not classified as medically necessary), while expensive, is within the financial means of most middle-class adults.

The average American says US healthcare spending, which is 3x to 20x that of other OECD countries on a per capita basis, is way too high.

The average American also thinks they should be provided testing and procedures that their insurance deems medically unnecessary.

Try to reconcile these two beliefs. (Hint: It's impossible)

Maybe there's a bunch of inflated profit margins and people getting filthy rich off a poorly regulated market.