Earlier quoted context omitted.
I don't quite get what you mean. If the cross-origin server (to your app) wants to be consumed then it will respond with the correct headers. And if the server is under your control then you can configure it so.
For non-browser apps the server doesn't have to explicitly allow it. A simple curl can access any server it wants. If y browser based apps wants to access another server, that server needs to be configured to allow it (because of the Same Origin Policy) and how many servers do you know that allow anybody to access them via CORS? So take for example a WebDAV server. In theory, you could build a web based app, that can…
Edit: Unless you don’t consider it ”cross site” if you control the API server?