Brad's point that:
The way things are going, in the future people are going to be choosing to spend X percent of their income on health care. X will get larger and larger over time, by choice. So let's say X is 40 percent. From one standpoint, it really doesn't make a difference whether you pay 40 percent of your income for private health care, or 40 percent of your income in taxes that then go to government-administered health care.
That's a very specific standpoint Brad's using. Because paying for government-provided health care leaves you in an enormous pool that guarantees you access to these procedures, no matter their cost and no matter your income. Private insurance, however, is different. If you want comprehensive health care, you have to buy into (or have your employer buy into) pretty expensive plans. For many, that much income simply cannot be spared and, thus, they simply won't have access to many of those treatments. To even try and get close to the top plans, poorer workers won't be paying out the same percentage of their incomes as richer workers, they'll be spending much, much more. The reason single-payer is worthwhile is precisely because everyone pays out roughly the same percentage of their income (with some income brackets a bit more and some a bit less) and receives comprehensive care in return.
Update -- The more I look at this post, the more I think I have Brad's point wrong. He knows health care way better than I do, and wouldn't have overlooked this. So I suggest reading his post in full, as I'm well open to other interpretations of it.