I feel like this is a new trend where exchanges are trying to make users feel like holding coins on their own devices is risky.

This and what CZ said about the 99% of people and self-custody are lies. I have an opposite claim. 99% of people who lost cryptocurrency are people who willingly sent it to a scammer, either an exchange, a cloud mining service, a bitcoin doubler or a fake mixer.
Your crypto is not safe in the hands of someone else!
This is just a fabrication of possible trust in third-party service, as you have said, self-custody is the secured way to hold your assets, and exchange can never be a better alternative to self-custody.
If anyone said they lose their asset in self-custody, then there is possible personal involvement, and approval if not there is no way you can lose your coins in the self-custody wallet when you didn't send it out or grant another person access to your wallet.