You don't get to redefine 'federation' because you prefer an approach different than IRC undertakes. It's very much federated and always has been. Data transfer is in the RFC:

   2.3 Messages

   Servers and clients send eachother messages which may or may not
   generate a reply.

> where is this federated IRC you speak of?

IRC has the ability to form networks of servers which share identities and chat channels. There used to be a few large networks and many popular servers were part of one of them. Back in the 90s "being on IRC" commonly meant having a nickname on one of these networks.

>Also, where is this federated IRC you speak of?

Freenode is one.

>There's no cross-server identity

Your identity is your nickname.

> Why can’t we run more things on top of email as a backend?

Security, speed, and lock-in.

Email is hard to secure without using out-of-band mechanisms, and at that point if you're already not adhering to an existing standard you might as well write your own.

Email is fast for what it does, but it's not fast enough to handle the low-latency and interactive environment of something like Twitter. We don't notice this as much because so many people are used to using the same 2-3 email providers (heck, Google alone probably accounts for most personal email), but in a truly federated environment there can be noticeable delays. SMTP explicitly allows for this and provides mechanisms to handle it.

And lastly, building on top of email makes it hard to achieve vendor lock-in, which makes it hard to make money.