How health reform will gradually evolve to single payer system

Leaving aside the pros and cons of a single-payer system (SPS), I'm beginning to believe that a SPS would be an inevitable consequence of any health reform proposal that contained a public option (PO), even one as benign as the current version of the House bill. (See my previous post on good points of that bill.)
I'm basing the scenario on my long-time experience as an enrollee in a prototype health insurance exchange (HIE), namely the Federal Employees' Health Benefits Program (FEHB). FEHB has about 8 million enrollees, including current federal employees, their families, and retirees.
First off, I need to explain that the FEHB program is a regulated marketplace with open season at the end of every year, during which enrollees can choose among roughly 10 plans, depending on their place residence. Government subsidizes about 75% of the arverage plan's premiums (as do many employers.) Less subsidy goes to enrollees in richer plans. None of the plans are POs. All are private, but some are not-for-profit.
Here's what has happened to me over the 30 years of enrollment. When I was young and feeling good, I enrolled in a plan with relatively low premiums (never the lowest, cause I'm risk averse). As I got older and more needy, I opted for a richer plan, paying more in premiums but using health care more. Apparently, so did lots of other aging enrollees, because the costs of that plan began to skyrocket. And, that plan began to add draconian control features to the management of its benefit. And more and more doctors opted out of that plan's network. Finally, the costs got so high and my mistrust of the plan grew so much(especially in the past year) that I chose a low cost plan and paid more for visits and drugs than before. Overall, I might have paid more for health care (counting premiums and out-of-pocket) but at open season last December I was willing to take the gamble. This year, though, I'm torn, because the lower cost plan leaves me exposed to higher drug costs and less generous coverage of some services and devices that I might need in the coming year, given my decrepit state. So, right now I'm weighing a choice between two plans whose premiums vary by a ratio of more than 2 to 1. My choice is based on what I know now about my current state of health, which none of the plans can take into account in deciding to enroll me. That's the beauty of "open season" and "guaranteed issue."
Now fast-forward to a grand health insurance exchange, as envisioned in the House bill. That plan would also have a regulated market place with private insurers offering benefits that can differ within a defined range specified in the legislation. When I say "benefits", I mean things like the deductible, coinsurance or copayments, catastrophic limits on out-of-pocket expenses, networks of physicians, hospitals and other providers, care mangement techniques like prior authorization for expensive procedures, etc. An example of a limit on benefit variation is the requirement in the current House bill that every plan cover well child care visits with no copayment or coinsurance. (i.e., free well child care--costs would be covered through the premium assessed on all enrollees.)
Without a PO, the marketplace would behave similar to the FEHB program. People would check out premiums, networks, deductibles, etc., and would choose the best plan for them. Over time, there would be sorting of enrollees, and the costs of different plans might diverge. If the House bill became law, the young&healthy would enroll in the cheapest plan possible, while the old&sick would enroll in richer plans. This process would be mitigated to some extent because in the new marketplace, plans could vary premiums by age by a ratio of 2:1. (That's not true with FEHB, where we all pay the same premium.) So, in the House bill, the young&healthy would pay less for richer coverage and at least some might be induced to buy richer coverage.
Now, enter the Public Option (PO). Under the House bill, the amount that PO pays doctors and hospitals can never be greater than the average payment rates under private plans in the marketplace. Most likely the PO administrator will "negotiate" with doctors as follows: "We're paying Medicare rates. If you want to participate, fine. If not, hasta la vista." Lots of doctors might opt out of the public option, because right now Medicare rates are about 30% below private insurance rates. Hospitals may be stuck with the Medicare rates, though, because it could be very difficult for the major or only hospital in a community to thumb its nose at a public insurer. (I just don't know what hospitals will do.)
In any case, the PO premium is likely to be lower on average than those of private plans. Who will choose the more limited PO, with its more limited, perhaps less "elite" physician network? The young&healthy, of course. That will make it easier for the PO to pay for itself with lower premiums overall. Lots of young&healthies choosing the PO would mean that their premiums would be low, and the oldster's premiums would also be held down (by the 2:1 rule). Meanwhile, the private plans will attract us old&sicksters, and their premiums will be driven up. Eventually, some of the old&sicksters will give up on the "elite" docs and will enroll in the PO. This yin and yang will continue over time until, gradually, the PO (which still has the cost advantage due to payment of hospitals on Medicare rates) has become the behemoth. With lower and lower market share, private insurers will fail, merge, exit the market, etc., and real competition will be gone.
If you've read this far, I must tell you that I'm not completely sure of my prognostication. Competition is dynamic, innovation is inherent in markets such as this. I could be all wrong. That's why I'm not wringing my hands at the public option currently in the House bill. The uncertainty is great enough for me to say, okay, let's pass a law that makes health insurance affordable and get on with it. But, I'm mindful that the great long-term danger is the decline of the health care system into a single-payer system. Perhaps in the future I'll post something on why I'm so worried about single-payer system.