I get what you mean but I don't think this is the same thing. HTML has a DTD, something that people conform to when writing, so your <haiku> tag would not follow that guideline, whereas companies like Twitter can implement their own error codes as they see fit. See error code 420, Enhance Your Calm.[0]
Well, sure, just like I can create my invented domain name like hacker.news and use my own IP addresse 1.2.3.4 without being allocated them. The Internet interoperates by everyone agreeing to follow the same agreed conventions, but there is no rule that says you have to. The registry for HTTP status codes has no 420 code and could be assigned for a different purpose in the future: http://www.iana.org/assignments/http-status-codes
Yes, they can respond with 420. However, my browser does not have a predetermined response for that. Whereas if they respond with 200 or 302 or 404, all browsers know what to do; that's what it means to be a "standard".
Tangentially to your point, that's only true of the 4.x and earlier versions of HTML which are SGML applications, WHATWG HTML / W3C HTML5 is not SGML-based and does not have a DTD.