I've ranted about this before, and I'll resist the urge to ramble about it again, but the gist is: if there is an encrypted backup option, everyone who's not thinking deeply about it will just use it because it sounds better, and they will end up with no plaintext backup anywhere.
You're right. I actually just read that rant, but my mistake was looking at this from my point of view rather than from a typical user's point of view. I would use it by printing an unencrypted paper backup, and then just printing out this encrypted backup as another layer of insurance in case the unencrypted backup gets lost/destroyed while I still remember my password. But as you pointed out, the typical user would probably not bother with the unencrypted backup. The other solution you offered, where you'd hand-write an additional code, would do the trick for me.