Considering all fingerprint readers have their weaknesses. I would consider this method no more secure than facial recognition when we have had for a while, and with only a 2d camera image for the phone to work with it would not be hard to trick either. I would consider this a low security convenience lock. It will keep your small child out of your phone and you don't need to type in a code or password to get in.
As for worrying about taking the fifth on something, there are far easier ways to get things like recent calls you have made and when, Email passes through servers, etc. A search warrant presented to the carrier would yield your phone records.
12 Pubs, 12 Pints, what could possibly go wrong?
Meet you at The World's End
If anyone has helped you, hit the "Thanks" button.