And yet, all of the routers are not audited, and I presume you believe in the security of some applications that use them. In other words, the trusted base of the system does not depend on all of the components in the system (you start with the assumption that any closed components are hostile). The keybase servers are exactly the same.

The answer is that they do have things to hide: anti-spam/anti-scam systems, for example. The question is if they are hiding something that matters for security. You can determine this by auditing only the client.

Sure, open source software is great, and has many uses. In this case, it has no use in ensuring that keybase is secure. Somehow, you don't have to trust a great many components in the secure software you use on a daily basis, and yet you have to trust keybase's servers because.. reasons? And somehow this trust is important even though you'd still be blindly trusting that they're running what you hope.

I won't argue that some people would benefit from the server being open source, but to argue that open sourcing it has anything to do with security is just inane and FUD.