It could be semi-transparent, i.e. visible to members only.
And there are many types of insurance where privacy is not a concern. For example, pet insurance.
For some types of insurance, such as car damage, most of the info is in public databases anyway.
i think there is no need of anonomity in insurance field also also decentralzation can't make enable to invest others money in something. I don't get idea about how this can work. P2P insurance
I think P2P insurance would be easily abused, though. There would be very little way to enforce the actual payment of the covered costs, and someone could basically get scammed out of the money they had paid for the coverage.
I guess if there was a reputation system or something, then a P2P system would be more viable.