The state you tend to store is in the application side, so it still backs onto things like SQL databases in the end. You'd put another service in front of your Asterisk instances like OpenSIPS or Kamailio to distribute load.

Seems like a huge hack. What we really need is some kind of etcd for telecoms, where you just configure it and they replicate and share state automatically.

It's not a hack. Think of Asterisk as if it was an http server + backend code. How do you scale?

You scale horizontally using proxies (kamailio dispatchers), (what you would call "reverse proxies in the http world), and use external storage / database / logic.

SIP? This sounds like exactly what SIP does. Or at least a function of what it exposes

Asterisk is just another daemon. You could use etcd for it or Puppet or whatever to create config on the fly. On FreePBX you generally use MySQL/MariaDB.

Lots of ways. Usually externally, through a database. An Asterisk box processes and forwards calls - you can hook into a "master controller" that decides what is to be done.