But this brings up another question:
All of the paper wallets I've seen or used contain QR codes for each key, as well as a string of numbers beneath these keys. If these are the keys, then what is the point of encrypting something that is already in plain view on the wallet itself?
Well, you can generate a QR code from the encrypted private key to

Usually, an encrypted paper wallet contains both the encrypted private key and the address both in textual format as a qr code, so you cannot use the private key without either knowing or brute forcing the password.