This is to address those who use 3rd party keyboards and can't get the setting to 'stick'...
To correctly disable the handwriting mode:
The first step is where most people aren't addressing the iOS keyboard needing to be set as default as a condition of retaining settings after they are made regarding itself.
Crazy, I know.
Set iphone to default iOS keyboard in settings,
Open an sms conversation and tap the text input area to get a blinking cursor
Rotate to landscape
Tap the keyboard icon bottom right, type something, send it.
You may at this point consider yourself finished and designate your favorite 3rd party keyboard in settings, confident in the knowledge that you won't ever have to be blinded by a huge white screen when in another app in landscape and try to reply on the fly.
I use SwiftKey on both iOS and Android exclusively.