Sometimes, my MacBook Pro (2016, 13", macOS Sierra 10.12.6) would not let me unlock it with TouchID, saying "password is required to use TouchID".
Is there any way I could always allow TouchID to unlock my MacBook?
No there isn't - at least not yet.
The Touch ID rules for macOS dictate that each time you boot up or restart, or if you log out, you need to type your password to log back into your user account.
In other words, once you're already logged in, you can use Touch ID when prompted for your password.