Block chain technology could be used for this purpose. A whole incentive and payment system would need to be created for this purpose. But the per-user cost and maintenance could be made to be extremely low.
As impractical as this may sound, it wasn’t long ago that today’s cell phones were only a fantasy. When you remove all of the math and encryption algorithms, the concept is similar to making an announcement of your intentions in the town square full of witnesses who know and recognize you, before being allowed to do whatever a password alone would do. The only difference is that everything is recorded and no one looks at the record unless a need arises later. The block chain of transactions is the permanent record that can’t be modified because it is a part of the encryption algotithm that is needed for future transactions to unlock.
I think that a whole eco-system will eventually evolve around block chain technology. When there are sufficient programming libraries that allow a few lines of code to implement these types of authentication methods, then this technology will become common place.