OpenSSL is beyond repair. We need a new clean start, sane design and rock solid implementation with principles and following best practices.
We need everything after the comma, sure, but there's no particular logical connection with the bit before your comma. A drop-in, API-compatible replacement (or at least one where the bits of the API thrown out are carefully chosen and generally unused) with OpenSSL that isn't scary and has been vetted is by far the fastest way to get to the second bit. This is probably the best thing that could have happened to OpenSSL, and I predict a decent chance this will be the dominant branch in under a year.
Also, I think that an OpenSSL cleanup is needed even if we get a new awesome library too. We can't drop OpenSSL overnight, and as you said it's bad. So this at least make it less bad, until there's something we can switch to.
"NaCl ships with constructions that were just prototypes, and that shouldn’t be used any more."
What does "shouldn't be used any more" mean? Certainly not security, or djb would have released an update. Compatibility with other products? Something else?
For authentication, there is CurveCP.
People seem confident with OpenSSH's authentication mechanism. Why not use that?
At some point one has to trust that the IP address one is sending/retrieving data to/from is the correct one. That's easier said than done if some host wants to keep changing its IP address every few days.
The SSL PKI scheme (the SSL approach to authentication), as implemented for public websites, is not much of a confidence-builder, IMO. Opinions may differ.
If websites maintained consistent IP addresses and we could authenticate these machines using OpenSSH keys, I would be more willing to believe we could verify their "authenticity".