Of course the health insurance companies don't want to go out of business.  Its interesting that we even consider what they want when it comes to health care.  They have managed to institute themselves to that degree.

There is a lot to say for single payer.
1. Costs can be controlled. Medicare pays X for this procedure (there is actually some variation). Not $1000 at one hospital and $200 at the clinic down the street.  In fact, single payer gives you a handle to start understanding where the cost bottlenecks are.
2. One source billing not only eliminates the multiple insurance company requirements, it eliminates the personnel time needed to deal with them.
3. It creates less chaos in care.  No more trying to figure out options based on your plan, doctors group, and insurance company.