Cold storage does neatly avoid the issue of getting burned by an exchange; your crypto is only stored locally with a cold storage wallet, so unless it’s plugged in to your computer and accessible to the internet, it can’t be hacked. OTOH, you can simply lose the drive (!), and forgetting your password means that the crypto is likely inaccessible forever (!!!).
I’ve misplaced things before, but I don’t usually throw shit out unintentionally. So I’ve still got my old Tails drive that has somewhere around .01BTC in a wallet on it. Now if only I remembered my password for the persistent partition.