Hello, lawyer Qin. Our car had the same traffic accident. At that time, we only reported the traffic police, not the insurance company. It has been two months now, and I can still find insurance.
The traffic police's responsibility certificate can prove the cause of the accident, but it can't determine the degree of car damage. For example, if you think it is damaged, you may not meet the contract, which will also give the insurance company a reason to shirk it. Further reading: How to buy insurance, which is better, and teach you how to avoid these "pits" of insurance.