Why are Ajax HTTP Requests not allowed to cross domain boundaries.
Because AJAX requests are (a) submitted with user credentials, and (b) allow the caller to read the returned data.
It is a combination of these factors that can result in a vulnerability. There are proposals to add a form of cross-domain AJAX that omits user credentials.
you could simply add an img, script, or iframe element to the document
None of those methods allow the caller to read the returned data.
(Except scripts where either it’s deliberately set up to allow that, for permitted cross-domain scripting – or where someone’s made a terrible cock-up.)
Your can do XSS attacks without using this at all. Posting to third party site
That’s not an XSS attack. That’s a cross-site request forgery attack (XSRF). There are known ways to solve XSRF attacks, such as including one-time or cryptographic tokens to verify that the submission came deliberately from the user and was not launched from attacker code.
If you allowed cross-domain AJAX you would lose this safeguard. The attacking code could request a page from the banking site, read any authorisation tokens on it, and submit them in a second AJAX request to perform the transfer. And that would be a cross-site scripting attack.