In the U.S., if you are a full time employee, then you will generally receive health benefits from the company you work for. This is a legal requirement for large employers (50 employees or more) but is also often provided by smaller employers. Generally this involves the company paying a significant portion of private health insurance costs. For instance, our family pays approximately $220/month for medical/dental/vision coverage for two adults and four kids. Generally, even if not covered by an employer, if you are not making a lot of money, you will qualify for subsidized insurance coverage via the government.

When you are covered by private insurance, typically there will be a co-payment whenever you visit a doctor or hospital though this is not usually very much (e.g. $50 for a doctor's visit). There will also be a deductible which can vary greatly depending on what insurance you have (this could be from a few hundred to a few thousand a year).

In the U.S., approximately 8% of the population is uninsured. I assume for some portion of those it is voluntary vs. being unable to afford it.

One of the downsides of government health care is, as you mentioned, waiting times. For truly low priority things, this isn't a big deal. But, as one example, I know that in Canada it used to be that some Canadians would come to the U.S. for heart bypass surgery (paying out of pocket which would set them back anywhere from $70,000 to $200,000) because in many cases it was considered "non-emergency" and waiting times were long in Canada. This was a number of years ago and things may have changed since then but the point being that what the government considers "non-emergency" or "elective" isn't always something it is safe to wait for.