Climate change is a phenomenon of the Earth system, which is characterized by thresholds and non-linear change. This analysis considers the adequacy of insurance (in its broadest sense) responses to climate risk. This paper provides novel critiques of insurance system responses to climate change and of the attendant political economy perspective on the relationship between insurance and climate change. A complex adaptive systems (CAS) analysis suggests that ecologically effective (i.e. strong) mitigation is the only viable approach to manage medium- and long-term climate risk - for the insurance system itself and for human societies more widely. In contrast, we find that even the most substantial insurance system responses to date are generally adaptive and weakly mitigative. This analysis extends an earlier political economy perspective that explains the limitations of insurance system responses to climate change, but provides little guidance to the ecological implications of such responses. As such, this paper raises questions about the ongoing viability of the insurance system, and hence about the many aspects of human societies globally reliant on the insurance system as their primary risk governance tool. We conclude that the CAS approach provides new insights, which could prompt insurance system evolution in support of effective climate risk governance.