Thanks for the examples Sam, I follow the first part.
Well that’s not what I said. I said the insurance company doesn’t want randomness. Obviously reality is random and they don’t get exactly what they want. However, insurance companies put great effort into gathering data and weighing probabilities to predict what they can and minimize the risk. My whole point was that I don’t think an insurance company wants a random cross-section of customers. I think they want to filter out the high-risk customers and sign-up the medium to low-risk customers. An employee healthplan can help them do this because many of the highest-risk people are not employed (or not employed with a job that provides a healthplan).
Of course, they don’t want to turn potential customers away, so they sign-up individuals without company healthplans, but they charge them much higher rates. This addresses the pitfall you describe above, informational asymmetry.