It seems like the issue is that Apple blocks third-party keyboards from loading when the phone is locked. (third-party keyboards load fine in quick reply if the phone is unlocked, at least for me.)
If you try to do a quick reply from the home screen and the built-in keyboard is disabled, then you get the only other active built-in keyboard (Emoji, for most people.) Disabling third-party keyboards when the phone is locked is probably intentional on Apple's part, but clearly the default keyboard should come up when third-party keyboards are blocked, regardless of whether it's enabled or not.