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 99% 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!