“In what way or ways would it be most difficult for insurance companies to function successfully as sources of justice and defense against aggression?”
I don’t think insurance companies can function as sources of justice and defense. At most they can offer people pooled risk services. They can insure contracts, pay out instant restitution and collect damage payments from the insurance companies of losers in arbitration.
The source of justice in a stateless market anarchist society might be arbitration agencies, and I expect these would be independent entities separate from the insurance companies and defense agencies. In order for the arbitration agencies to retain credibility, they would need to maintain distance from the insurance companies, lest people think they were biased in favor of one or another.
The source of defense in a stateless society might be police, or defense, agencies. These would also need to observe a careful distance from the insurance and arbitration companies for the same reason.
Thus, perhaps the answer is that insurance companies would need to studiously avoid proximity to defense agencies and arbitration services in order to maintain maximum credibility and avoid the appearance of favoritism or conflict of interest. Integrity and impartiality are the most critical elements of free market justice and defense, since first force can not be used to compel submission. Only voluntary relations will stand.