If I were to implement my own OO programming language, static data would be the first thing to go. I can't find any compelling reason to keep it around.
Something that people may or may not undestand is that static really means "global". Seriously, I wish that languages like Java and C# simply used global as the keyword instead. Static methods are simply global methods that have a long name with a period in the middle (well, I suppose they are also scoped and are subject to access control). Static, final references to immutable objects are just that - they're global constants. Keeping a single definition of PI around is generally a good thing. And, you guessed it, static fields are simply global variables in disguise.
"But!" I hear you say. "But I need static fields to implement singletons!" Why do you want singletons? Sure, you might think that you will only ever want a single instance of a class. I think you're wrong. What happens when you want to do some unit testing? What happens when the requirements change.
At one point, I'm sure that Windows assumed that it had exactly one display. If singletons had been widely used then, I would not have been surprised if there were some singleton which kept the display's information (in actuality, it may have simply been a global variable). Today, we might not only have several physical displays, but we might also have multiple active windowing sessions on a single Windows server. How about mice? Surely, a system has no more than one pointer. Well, that's kinda true, but my coworkers and I wish that we could get a second pointer on the screen for our pairing sessions. What about my Wacom tablet? And my friend prototyped a game that was controlled by using two mice. Singletons are the antithesis of what the Dependency Injection folks have been telling us.
If I were designing a language, I would want the programming language to encourage good programming practice. Since I'm the one designing this language, I get to choose what is good and bad. And I say, "down with singletons!"