I'm paranoid enough about third party custody that I always withdraw coins from exchanges whenever possible. And I know that insurance is expensive, and that money has to be recouped somehow......higher commissions, fees charged to me as a customer. So I feel I'd be subsidizing those who irresponsibly use the exchange as a wallet.
The insurance for an exchange is intended to cover the cold storage funds and protect the exchangeand by extension, users/investorsfrom theft via hacking, employee theft, or even physical theft. If the exchange is insured, and a theft from the cold storage occurs, then the insurer will reimburse the exchange who will then provide the funds to users/investors.
I imagine there might be a lengthy legal battle before the insurance company actually pays out. Coinbase has its hot wallet insured, but that's only 1-2% of their total crypto funds. I assume if you're insuring cold storage, we're talking about a much larger percentage of total funds in custody, maybe even 100%? Cold storage insurance (and crypto insurance in general) = completely uncharted waters. Thus I think insurance companies in this position have a lot of added incentive to reject future claims and go to court over it.