The physical form factor here described is "convertible slate". However, as someone who has spent a lot of their computer time using convertible slates (starting with a Compaq Concerto and a pre-release Dauphin DTR-1 back in 1992: yes, I was using "Windows 3.1 for Pen"), I will point out that with all of the circuitry in the slate the keyboard has to end up irritatingly poorly/awkwardly weighted (as it is way too light to make holding up the screen make sense) and is also bothersome to bring you (its "yet another fidgety component").

So, I then look at my 11" MacBook Air, and frankly: the dimensions are almost the same as the original iPad. It is /slightly/ wider (due to the constraints of having a full-size physical keyboard with keys that recess and also various ports such as USB that require a certain amount of clearance inside of the device, which is already so thin that these ports barely can exist in the device at all), but if USB is supplanted by something like Apple's Thunderbolt (convenient, huh), they could make it slightly narrower and slightly thinner.

I then argue what you're really going to end up with is a device more like the NEC Versa (1995-ish) or ThinkPad X61 (more devices I've owned), where the screen rotates around and folds back down backwards. This way, you always have the keyboard with you, and it can "take the load off" the screen part by having real circuitry in it (thereby giving it enough heft to balance the screen easily), which in turn allows the combined size to be smaller (as otherwise you are having to artificially increase the heft of the keyboard).

Apple, in fact, has been looking at such designs. We see patents from them for various ways of building a convertible slate for a while now. The original design had the screen hinged along the edge of the keyboard, where it could kind of slide down the case towards the end, and then fold back (away from you, as opposed to towards you) onto the keyboard, turning into a slate (which has the property that the screen's orientation doesn't change during the operation), but in 2011 we see the more traditional "rotate".

http://www.patentlyapple.com/patently-apple/2008/07/apple-re...

http://www.patentlyapple.com/patently-apple/2011/11/apple-wi...

The 2011 design also makes it clear that this device could have a cellular modem in it, which means that were it to exist it would compete with a 3G iPad. That brings us to the listed constraint of "run apps written for iOS". Truly, however: much like you don't actually want a case that can house a keyboard and attach it to an iPad, you also don't want to be able to run iOS applications; the mistake in both is to take what you have now, assume "I can't have it both ways", and then come up with some kind of band-aid solution.

What you really want is to have a single set of applications that work well on either form factor due to a set of unified interface primitives. When you "convert" between a laptop and a slate, you don't want to be running a different web browser and a different word processor: you want there to be a seamless set of rather subtle changes to the apps you were just running (if any changes are required at all: in an ideal world you would want no changes, but there are practical concerns), allowing you to maintain mental state.

Again, this is the direction Apple is headed. In Lion they have started moving desktop Mac OS X to a world of full-screen applications, just like on iOS, and are borrowing many of the UI elements. They reversed the scrolling direction (to make the gestures common) and removed the scrollbars (which already aren't present on iOS for various reasons). Gestures are now permeating more of the applications, and with just another couple years of this, the difference is going to be quite slight; and yes: they have another patent on it.

http://www.patentlyapple.com/patently-apple/2010/11/apple-wi...

Really, the only thing left would be to figure out how to unify the App Store experience. Ideally (for Apple), the resulting ecosystem would be quite similar to the situation on iOS: a closed store that Apple controls, with careful "security" measures at all levels to keep the user from "messing up" their device with software that wasn't centrally vetted. This would be accomplished with a combination of protected firmware and sandboxing of all applications, each of which would be isolated to their own state.

Well, with the advent of the Mac App Store we see Apple offering the same unified experience, and with Lion we saw them adding sandboxes. These sandboxes eventually became a required part of the workflow, and with Mountain Lion they are getting tighter. Meanwhile, Mountain Lion has added the "only from App Store" switch: defaulted to off (for now), but with another half-way setting, "only from registered developer" defaulted to on; even I felt this was ahead of schedule ;P. Again: we only need to look forward another couple years.

tl;dr I believe Apple's behaviors (and patents) agree: their goal is to provide this.