(Which is in turn made harder by IPv6 public addressing, where you can’t just block the private IP range because you might not be behind a NAT in the first place, instead only behind a firewall. So your address A::B, can route to your Intranet peer A::C, which isn’t public-routable, but is a public address. But there’s nothing, other than the firewall, that says that that’s not a public address. It’s a hard problem!)
evil.com can set a short DNS TTL, and after you access it, it can rebind its address to 127.0.0.1. Then subsequent requests to evil.com go to localhost (e.g. fetch("evil.com", ...) on evil.com will go to 127.0.0.1 if the DNS rebound successfully).
Caching a website's IP on first use doesn't help, either, because it breaks long sessions on websites that use DNS rebinding for legitimate purposes (load balancing, fallover).
The only real way to fix this is for the local webserver to check the Host header on the HTTP request... or look at IP addresses. But building a global registry of IP addresses is hard, so we're stuck with trusting application developers (and malware writers) who run servers on localhost to use good security practices.
The process is different enough from cookies to warrant another large discussion about how to do it, with plenty of trial and errors. But the stakes are much lower, as in the worst case the user will get a dialog, instead of a site being broken.
How shall origin be defined? I can envision the likes of Microsoft which have many, many second-level domains making calls between them.
We can’t allow the site itself to grant access. How would this be managed, other than “please stop and think what a domain name is supposed to be before spraying your product across twelve of them?”