[ars_technician]

That's an oversimplification. The field of cryptography has advanced by orders of magnitude since DES and RC4. Each time one of those breaks, we abstract the weakness into a class of vulnerability that the next algorithm will be immune to.

>There is actually no precedent of a cryptographic system relying on computational hardness surviving for more than a generation.

That's because cryptosystems relying on computational hardness aren't that old.

>And given that our fundamental theoretical understanding hasn't really evolved beyond, "we think a bunch of these problems are hard", things are likely to stay that way for a while.

These assumptions haven't really broken though. You give an example of DES, but that doesn't rely on computational hardness assumptions. Asymmetric crypto with a trapdoor function does. There hasn't even been a big breakthrough in the original prime number factorization assumptions of RSA/DH.