Why do browsers apply the same origin policy to XMLHttpRequest? It's really inconvenient for developers, but it appears it does little in actually stopping hackers. There are workarounds, they can still include javascript from outside sources (the power behind JSONP).
It seems like an outdated "feature" in a web that's largely interlinked.
Because an XMLHttpRequest passes the user's authentication tokens. If the user were logged onto example.com with basic auth or some cookies, then visited attacker.com, the latter site could create an XMLHttpRequest to example.com with full authorisation for that user and read any private page that the user could (then forward it back to the attacker).
Because putting secret tokens in webapp pages is the way to stop simple Cross-Site-Request-Forgery attacks, this means attacker.com could take any on-page actions the user could at example.com without any consent or interaction from them. Global XMLHttpRequest is global cross-site-scripting.
(Even if you had a version of XMLHttpRequest that didn't pass authentication, there are still problems. For example an attacker could make requests out to other non-public machines on your intranet and read any files it can download from them which may not be meant for public consumption. <script> tags already suffer from a limited form of this kind of vulnerability, but the fully-readable responses of XMLHttpRequest would leak all kinds of files instead of a few unfortunately-crafted ones that can parse as JavaScript.)