Never ever keep your coins in an exchange
I'm fairly more moderate on that one.
Yes, a true hodler will never hold coins on an exchange. Exchanges are cracked, exchanges do go bankrupt, it has happened several times that people lose all their holdings due to this.
At the other hand, exchanges are typically the best gateways for getting in and out of crypto; it does make sense to use those gateways, hence the recommendation should already be modified to "keep your coins as shortly as possible on the exchanges".
I'm selling crypto locally and domestically, on Localbitcoins and other sites - quite often I meet customers face to face and talk with them - I'm of course asked all kind of questions, and I have actually started to recommend people to keep their Bitcoins on Localbitcoins rather than in personal wallets, because:
Localbitcoins has been around for a long time, they seem fairly security-conscious, they are for sure raking in bitcoins, they for sure have a huge cold storage of coins. Of course there is always a risk that an exchange will pull the plug and disappear ... but I think Localbitcoins is one of the least likely candidates to disappear.
Keeping the bitcoins in a personal wallet also have risks. For people like me, those risks are mostly manageable - but I actually believe that for the average of my customers it's safer to keep the bitcoins on Localbitcoins than in a personal wallet. I usually recommend hardware wallets (even if I've never used one myself) or paper wallets, but there are even stories on people losing their bitcoins due to problems with hw wallets or compromised paper wallets.
Due to the capacity ceiling, the cost of moving Bitcoins around has been very high. Right now it's very cheap to move bitcoins around, but this may change again, and there seems to be no upper bounds on the bitcoin transaction costs. Keep the bitcoins on an exchange, and one can exit without having to pay any transaction fees. Personally I keep most of my bitcoins on Localbitcoins - I prefer to do my outbound bitcoin transactions from Localbitcoins those days - they are very good at getting their transactions out for cheap and one can still be reasonably sure the transaction will be confirmed. (I also prefer to have my Bitcoin Cash in my cellphone wallet, ready for spending, like in the good old days).
I wrote my own post around the same topic the other day, but with a bit different tips.