Party responsible for marine insurance in Local L/C CIF transactions

As a shipper (manufacturer), I am conducting Local L/C transactions with a domestic trading company under CIF Incoterms. The transaction structure is Shipper (Manufacturer) → Domestic Trading Company → Overseas Buyer, and the transaction with the domestic trading company is a Local L/C transaction under CIF terms. In this case, shouldn't the insurance premium be deducted from the unit price, and the actual marine insurance be taken out by the domestic trading company? If that is not the case, I am curious about the basis for requiring the shipper to arrange the marine insurance.