> When an app on another server is started up, it must be done from a shell
That's a no-go for many setups. It doesn't integrate well with how Linux distros usually start services (systemd, upstart, sysv init, ...), and means you have to have another way to manage dependencies between your services.
> When an app on another server is started up, it must be done from a shell (we use cap) which has an SSH agent forwarded to it. In order for the app to get its database passwords and various other secrets, it makes a request to the secret server (over a TLS-encrypted socket), which checks your SSH identity against an ACL
At this point you could have used ssh right away, no? Any reason you used TLS + checking SSH agent instead?