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Either way in exchanges, you already had the risk of losing your fund anyway. I personally never had any cold storage, and I am just having a separate machine that is for my own desktop wallet. It won't be used for any browsing purposes that would risk of getting hacked or getting infected by spy/malware. Kind of an alternative, if one also does not want to spend too much in a hardware wallet.
That is rather our choice to buy an expensive hardware wallet if that is really a need for us. I'm still using an online wallet and custodial wallet in our country but so far, I have no issues about losing control of my account, maybe that was because I don't entertain emails coming from the unknown person especially when sending links. I've been careful in keeping my computer not to use by others and I don't allow them to touch/borrow this.
It is either what kind of wallet we use, that certainly it depends on how we handle them. But not to put them on the exchanges as the chances of getting hacked is bigger than keeping on our controlled storage.