You don't want that key to be in the box. Because of Apple printed it, they know it.

It's better if the key is generated when you already have the phone.

Well if the alternative is the current situation where Apple has access anyway, a key that Apple may know is still a better idea.

For even better security they can instead provide an NFC smartcard or hybrid NFC + USB (like a Yubikey) where the key is stored in hardware and can't be extracted.

Apple also pushes software updates to the phone, so does it really matter? I'd be more concerned about a third party intercepting and copying the key.

Far easier to develop a culture of using something physical like yubikeys - over flimsy cardboard QR codes. The key metaphor makes a lot more sense that way, too.

So you are suggesting making everyone life more cumbersome with the very likely potential of losing all the data on your phone because you lost a piece of cardboard or forgot a key for which benefit exactly? Being hypothetically safe for government scrutiny concerning information they could a dozen other way?

I really like E2E encryption of messages with proper backups on my end. It's good to know the carrier of my messages can't scan them for advertising purpose. But for my phone if I know there is no way to easily get the data back if I have an issue that seems like a major hassle with very little upsides.