It could. But it hasn't been done yet. And as rcxdude stated, it would need to be done in such a way that you can't create a fake secure textarea using HTML.
Perhaps when focusing on one, all other script on the page stops, no events or timeouts are triggered, everything other than the secure textarea is ghosted out, and something big and obvious in the browsers chrome lights up to show you that you are actually focused on a "secure textarea" and not a normal one.
Perhaps when focusing on one, all other script on the page stops, no events or timeouts are triggered, everything other than the secure textarea is ghosted out, and something big and obvious in the browsers chrome lights up to show you that you are actually focused on a "secure textarea" and not a normal one.