While this generally is the consensus, and definitely is recommendable,.. if his PC gets compromised, it doesn't matter whether there is the mnemonic code stored in a text file or not.
If there is a wallet installed, it is compromised. And the next time it is being opened, the adversary has access to the private keys / coins. Regardless of where the mnemonic code is stored.
When using a desktop wallet, you have to assume you can protect your device properly. Not storing the mnemonic code on it is recommendable, but it doesn't make it much more secure overall.
It is important to not get into the state of perceived security.