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Not sure I buy this. Lack of cryptography doesn't even need to make password based authentication impossible.
Firstly, to compromise a system, even one that's not encrypted, you must be able to execute arbitrary commands. A system that's locked down and limited to a few hardened interfaces with the rest of the world is naturally robust to this. You can try pulling out the memory and read/manipulate it directly, but there are low tech (put the components behind steel plate) and high tech mitigations that don't rely on cryptography. And if you're in a position to circumvent those, you can probably just replace the controller of whatever system you're trying to compromise with your own controller anyway.
Secondly, P=NP would make reversing hashes doable, but when you're trying to break into a system you (usually) don't have the password hash you're trying to guess. So you're stuck trying to guess it (unless you can read it from memory, see point 1), and that's going to take forever regardless of P vs NP.
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