In mathematics, there is often a large number of ways to prove a fact if that fact is a universal truth. For example, there is a large number of ways to prove Pythagoras theorem. If something is true, you can look at it from many angles and arrive at the same fact. However, in cryptography, this hardly ever true. If you had lost your private key, you cannot access your assets, or decrypt messages, even if there is other strong evidence that they are yours.
The ability to prove things is critical to creating a world of fair credit and access to information. If you had ever lost a password, or wallet of bitcoin or other digital currency, or simply your data locked under your encryption key, you know how unforgiving is the fact that you only have one way to prove facts. For example, you may have proofs such as transaction records in other databases, governmental records and legal bank transactions, even people's memories, but that all doesn't count to recover a credit on cryptographic systems, if you do not have your private key.
A multi-method provability of cryptographic facts therefore would be a desired property for cryptographic methods.