>This isn't how cryptography engineers think about cryptography.
That is my point exactly, it should be how they think about it. Attacks to the cryptography math itself are only a single vector, the software implementation of it is going to have holes not to mention those beyond it from the hardware at the chip level to the firmware that runs it there are vulnerabilities well outside the math itself.
These are cryptography researchers, talking about cryptography vulnerabilities. The premise, both of the paper and to the comment upthread, is: we should have fewer cryptography vulnerabilities, and could accomplish that by not having people come up with random authentication and key escrow protocols.
For instance, the weird authentication scheme that gives rise to the RSA key recovery attack --- that problem is what PAKEs are for.