Generally safer with an exchange I would disagree with, you’re at the whim of whatever is in the TOS for that exchange, it’s not a bank or securities broker. If you’re relatively good with keeping secrets/passwords then setting up your own wallet should be easy.
It seems like exchanges kind of are counterintuitive for a decentralized financial product (for holding your crypto). One could argue that exchanges that fail when people are selling off a lot of volume might not have a good business model. My naive brain thinks an exchange will make money on transactions so it shouldn’t matter if the exchange from crypto_bucks to USD is different. If volume falls drastically then maybe your operating costs are too high?