The corners are the top second to top fifth most easily and reliably accessed points on any given screen, making them the best place to place interactive elements. This is not less inherently intuitive than having users aim for a Start button and require them to click on it to do things like...shut down. In addition, the effective hit area for a corner is immensely larger than that for a button - most people actually click the corner when they go for the Start button instead of somewhere in the middle.
By intuitive you mean, have the user jab their mouse into every corner of the screen to reveal hidden items?
Users have already been habituated to contextual actions that are brought up by right-clicking. Aside from these actions, they interact primarily with content in whatever program or application they are using. For example, in a web browser, the primary interaction is passive: you view the content area that displays the web page about 95% of the time if not more. Substantially less time is spent on navigating the forward and back arrows, refreshing the page, printing the page, looking at the source code, etc.
By intuitive you mean, putting the user in a full screen app with zero visible menus?
This will be something that people get used to, but the series of actions to initiate a search is completely identical to that which has existed in the prior two versions of Windows. Ever since Vista was released, a search can be initiated without looking at the screen: hit the windows key or throw the pointer and click the bottom left corner of the screen, then start typing.
By intuitive you mean, letting the user search from the start screen by just typing, yet never informing them that they could do so?
Users are familiar with right-clicking to bring up additional options by now. This has existed in Windows for a substantial amount of time.
By intuitive you mean, have an actual "All apps" screen yet have it hidden until the user "Right clicks" ? (something a user does very rarely)
I don't recall having to look very hard to get to the time settings. If you search for "time" in settings, the first hit is the right one.
By intuitive you mean, set the computers timezone to pacific standard time by default never giving the user the options to configure it during the first boot (like all previous versions of windows) and never explaining to them how to configure it after they have arrived in windows.
The first thing most people will do is click somewhere.
By intuitive you mean, covering up the actual log in box with a pretty picture and the time, never informing the user they can just click to get back to the login box.
It looks like every single one of those options is available from the Start screen as well.
By intuitive you mean, still give the user quick access to key functions of the system by right clicking a hidden box in the bottom left. Yet never explaining to the user their is a hidden menu in the bottom left, and that you have to right click it to get the list of key functions.
We've never informed users that they have an "a" key on the keyboard and that pressing it will result in an "a" being typed into any text box on the screen either. Strangely enough, they seem to have picked it up somehow.
By intuitive you mean, letting users bring up the start screen by pressing the "Windows key" on the keyboard, yet never informing them they even have a windows key on their keyboard and that by pressing it will activate the start screen.
No less obscured than previous versions of windows.
By intuitive you mean, have a CRAP ton of useful shortcuts for accessing things quicker on windows 8 yet never even inform them that these shortcuts exist. (most users don't even know they can press control + c for copy)
It really seems like you're basing these statements on the case where a user has never seen a computer before, and an obvious result of that is that there is a learning curve.