I thought I had the same issue, but before I chalked it up as a bug I wanted to try something first. I only tried this a couple times, but it worked every single try. Quick reply and the send button pops up when you use Touch ID to unlock but never press the home button - meaning the lock button in the center, on top is gone. When the lock is present, it never allowed me to send a message, it just let me view it. It's the same when swiping a notification to open it, the app never opened unless I already used Touch ID to unlock the phone. I hope hat made sense...
Next time have someone text you, use Touch ID but don't hit the home button to unlock the phone (the lock is not present) - you should be able to reply. Then try it again, and don't even use Touch ID (the lock should be present still), you shouldn't be able to send anything...