Too late to edit my post above...
Under Settings>Accessibility>Home Button is the setting "Rest Finger to Open". This is the key clue.
Notice it says "Rest Finger to Open" and NOT "Rest Finger to Wake".
On devices *without* a Home button, the device is wakened by tapping the screen (since there is no Home button).
On devices *with* a Home button, the device is wakened by clicking either the Home or Top buttons.
If you have Touch ID enabled, enabling the "Rest Finger to Open" setting will read your fingerprint immediately after clicking the Home button. If your finger is already resting on it, the device will read your fingerprint and unlock the device.