Well no, I explained why - it dilutes the risk pool. But take a glance over the history of insurance article on wikipedia and notice that the trend at every conceivable juncture was to expand the risk pool (but to try and drop bad risks). Architects of social welfare schemes obviously realized that when you are still responsible for a bad risk, the best answer is to include everyone.
the best possible insurance scheme for a country is single-payer, where everyone is part of the same risk pool
If this were really true, why stop at insurance industry? Why not leverage the awesome economy of scale by getting rid of the petty competition between Coca-Cola and Pepsi? Ford and GM? This was, actually, attempted already — to miserable results.
The numbers speak for themselves: the overhead of Medicare is about 6%. The overhead of a private health insurance company is closer to 20%. The insurance industry - particularly medical insurance - does not work like any other product. It's non-optional for the users, they have no negotiating power at the time they need it, and everyone will need it. Which means you can't simply boot people off of it consequence free since doing so usually kills them.
You are right in that size does matter for insurance companies. But only to a point. A company with 200 mln customers is not appreciably more efficient, than one with 100 mln. Having such companies compete with each other is much better for all the 300 mln, than to force them all into a single 300 mln-customer monopoly — governed charlie rangels and nansy pelosies to boot.
Competition requires innovation, innovation has to operate within the constraints of physical reality. Insurance is not a technological enterprise by and large, there's no new inventions which mean someone can gain a competitive advantage - you can't sink money into R&D and come up with a cheaper, better product. The only things you can do are figure out new ways to drop people from insurance - ideally after they need it. Which is exactly what US health insurance companies have been innovating on.