"I would think that the real problem is Microsoft's unwillingness to become something completely new, something other than Windows and Office."
Inability, perhaps. Unwillingness? You're out of your mind.
Microsoft has had their fingers in smartphones, music players, search engines, touch computing, web mail, [you name it] for YEARS. And they are not just dabbling... they have poured billions into these areas, trying to come up with something that gains traction.
Microsoft doesn't make "the occasional try" at innovation, they are a veritable firehose of attempts to innovate. Microsoft Research is HUGE (and well respected within the research/academic community) and as I mentioned above they spend billions every year trying to develop new products and break into new markets.
The fact that Microsoft's efforts in this area have been largely unsuccessful over the past decade doesn't mean they aren't trying or aren't willing.