There are times when choices are spurious. For example, the choice between one health insurer and another is not constructive. What matters to a patient more than anything is the choice of doctor and treatment (along with their availability and quality), not the choice of insurer. Indeed, a diverse market of insurers fragments the pools of doctors, treatments, and patients. Even when looking to the immediate goal of insurance, the more fragmented the pool of the insured, the less the costs can be smoothed out across the population. The worst health insurer is a small, local one with few doctors and dictated treatments. Such an insurer has little choice but to pay out as little as legally possible.
Do you see the simple idea? Some options increase freedom. Others secretly decrease it. We need to focus on finding and maintaining options that increase freedom. Sets of options that ultimately reduce choices and coerce traders should be eliminated.
I have no particular prescription for how many health insurers would be the right number, other than that, based on the above, one would seem to be the best number to start with, and if one isn't enough then it could be increased until it's enough.
We don't have forty thousand internets. We have one. (The local instances of the internet (intranets) that are not connected to the global one may work the same way, but they are not easily confused with the real internet. If I navigate to Wikipedia and Google and Amazon and get nothing, but I seem to have an IP connection active, it's fair to assume I'm not connected to the internet.) Having forty thousand internets would not be better than having one. It would be a dramatic downgrade. It would reduce options for navigating and sharing information to a sliver of what we enjoy now.
So why not have one health insurer? If one isn't enough, try two. If two isn't enough, try three. Having one insurer, or very few, would seem to maximize the number of doctors available to everyone. Then we can focus on paying medical staff for eventual outcomes and quality of care, rather than for the technological and capital intensity of the treatments.
There's nothing magic in what I'm saying. It seems mathematical, but surely it's abstract and short on detail, and I could be deceived. Is the abstraction true to life?
