Is it important to have an unencrypted backup of the private key?
It is important to be able to recover your private keys using only tools you fully control. That protects you against failure of infrastructure you would otherwise need to transfer your funds. There are lots of stories of corrupted backups, unreadable backups, and backups that didn't actually include the private keys.

Storing your private keys unencrypted on paper is one way of doing this. They can also be stored electronically in encrypted form, so long as you have reliable access to the encryption key and decryption tool.