Excellent read, Patrick.
I think it really comes down to wanting a new entry in a franchise, or from a specific creator (regardless of medium) that has new ideas or makes meaningful changes. It doesn't have to be totally reimagined or even changed drastically, necessarily.
I think Call of Duty is incredibly played out at this point, but I can't say I wouldn't play another one (my last being Black Ops) if they made enough changes that seemed positive.
The issue is that a lot of particular franchises have a very specific audience. There's no room for that sort of freedom in Call of Duty's development cycle.
It's got to be pretty difficult to balance expectations vs. possibilities in creating something new with an established IP. Seems to me like there is a point where a property is just the right distance from the popular consciousness to allow for an injection of fresh ideas.
It's also possible to avoid this if the property in itself is malleable enough. Another commenter was bored with Super Mario games but I think Nintendo is the ultimate example of this type of creativity.
Not every Mario (or Zelda) game is well-received, but most are. The New Super Mario Bros. series is pretty boring and lost all novelty after the first title, in my opinion, but Nintendo is doing wonderful things with games like the almost universally acclaimed Super Mario 3D Land.
Not every property (and their demographics) will allow for this sort of thing. With enough time and money, anything is possible, I suppose, but in reality it comes down to the likelihood that it would sell.
Oh, and kickstarter for the lucky projects.