It's not a disabled feature but a bug.
If you have multiple approvers (like my wife and I), then you can confirm that the issue only occurs if you *cancel* the Touch ID approval even just once.
From that point forward, it will only asks you for a password, never Touch ID anymore. But for my wife, it still works. So it's a bug.
You must go to the following link: Contact Apple Support
Select iPhone, then iTunes/App store, then "This is not listed", then select email or chat/phone and enter "Touch ID no longer prompted to approve family purchase".
They might tell you to reset all settings and/or restore the device but none of that works.
Then they will escalate to Level 2 support as a bug. If we all do this, then it'll get fixed in the next iOS update.
Please pass the word around.