I believe P ≠ NP as much as anyone else. Nevertheless should we worry about trust we put in complexity?
You don't need the full power of P = NP to break cryptography. I don't worry about quantum computers breaking RSA and related protocols. It won't sneak up on us--when (or if) quantum computing gets anywhere close to factoring large numbers, we'll figure out a strategy to change our protocols and to protect the information we already have. However if someone comes up with an algorithm tomorrow that cracks AES, we'll have a crisis on our hands as AES is so well used the algorithm is embedded into computer chips. Perhaps we can mitigate the damage before the algorithm spreads or at take our information off-line until we develop new solutions.
But what about blockchains, the technology that underlies cryptocurrencies such as Bitcoin. A blockchain consists of a series of transactions collected into sequence of blocks, where each block consists of a hash of the previous block with transactions themselves hashed and often encrypted with public-key cryptography. One would hope that breaking the cryptography would be caught quickly and we'd still have a legit record of transactions saved somewhere. The transactions themselves might be compromised especially if anonymity was built into the system.
Bitcoin itself, as I write this, has a total market cap of over $250 billion based fully on cryptography. The cryptography will probably hold up, Bitcoin investors have more to worry from bad implementations or the pop of a bubble of unrealistic expectations. But as we watch so many exciting advances in computing tackling challenges that we would never have expected to get solved, should we continue to build our economy on the hope that other advances won't happen?