1) How would miners find out that it was actually Alice in-person who used her personal key?
2) How do miners know that Bob is actually a living person?
3) How could miners know that Alice didn’t sign the papers at gunpoint?
Miners only know that the math adds up. If someone manages to put fake data on the blockchain it would be treated as authentic as the rest data. To conclude, blockchain cannot guarantee the authenticity of data across-the-board.
What actually makes sense is the data reconciliation between independent parties that blockchain allows for. It will change the very ecosystem of our interaction with the middlemen (in our case, notaries) because there will be a certain amount of the independent ones who will be fulfilling certain work. The result of the work will be more authenticate because independent parties are less likely to collude with each other.
The example. Imagine some blockchain-based debt-obligation registry. Bills of debt have much more weight when are notarized. The blockchain ecosystem will allow for the multiple verifications of one document by various independent validators (call them whatever you want: oracles, notaries, middlemen, etc). In this way, you have much more guarantees that all the documents (bills of debt, in our case) are authentically digitized. They are not just legitimate according to some centralized entity (that practically can legitimate anything it wants to) but are actually competent and consistent because are verified by the independent parties.
The direct work that notaries do won’t go anywhere, rather, will be transformed. To be precise, the very way this work is done will change. That said, some of the processes will become more automated and will exclude the human involvement. For example, the verification of signatures. Machines may well do that in the near future. However, some processes cannot replace humans with algorithms, such as determination of facts from the real world.
Illustration by Katerina Krashtapuk