You made good points until you said "world-class productivity software". The iPad absolutely does not have world class productivity software. That comment is laughable. I love my iPad air 2 and I use it almost exclusively these days. MS office and pixelmator are great apps and they work very well but they are absolutely nowhere as efficient or powerful as their desktop counterparts and by no means are they "world class". Anyone writing a research paper on an iPad (even with a real keyboard) is going to have a horrible experience next to someone using a chromebook or Mac/windows laptop.
Oh, I didn't mean to say they're truly desktop-class, but they do have extremely capable productivity software. The problem is that you can't really interact with it productively -- writing a word document, making a powerpoint presentation, etc. doesn't really lend itself to the iPad or to touch-interaction in general.
Now, if the iPad had a real pen as an input device, or a physical keyboard as convenient as the Surface's, we would be able to be much more productive with the devices. Maybe it still won't match the desktop in all cases (maybe it'll be even better for other cases), but it'd be much more realistic than the current proposition.
Apple should really embrace the NUI (Natural User Interface) paradigm in general. This is something Microsoft is currently doing better than anybody else. NUI is about computers becoming more human in their interaction -- using a combination of interaction methods such as touch, speech, pens, whatever; all of which can be used interchangeably so that the computer fits human beings rather than the other way around.
Apple currently does touch and some limited speech interaction, but other input devices like pens and keyboards seem to be treated rather apathetically. They would make the iPad a better product and a much more realistic business tool than it currently is. Not a desktop replacement, but something which has a place alongside a desktop.