Government gives power to insurance (and to other healthcare related companies, and really to a myriad of other players in other industries) primarily by:
- introducing regulations that make competing with incumbents nearly impossible
- giving tax breaks to favored corporations and behaviors
Why does government do this? Again, because the good people in government have been corrupted by power. The people they give power to help them stay powerful by giving them campaign contributions and other favors. It's a vicious cycle.
I'm not sure how to answer your last question, "what actions do you think companies might take to benefit customers if not for government involvement?" when every corporation does things to benefit it's customers. That's why any and every corporation exists, to benefit it's customers. Customers are anyone that benefits the company. Apple makes great products that benefit their customers without the government telling them to do it. In industries like healthcare in the U.S. right now, we are not the people who are primarily benefitting the corporations. The way things are bought and paid for right now I don't think we benefit health "insurance" companies at all!