3D globes and the like are very useful for quick visualization purposes. You can instantly see Global Level and Continental Level data, and spatial relationships and distances are easily understood.
However if you think about it, you don't really need a Globe foe every such case. As SS_Rebelious has mentioned, a Globe on a Flat Screen, is basically an Azimuth Projection. For example, Just look at the Maps on this page, which show the distance from North Korea.
If you think about it , Static Globes aren't really a good visualising tool, because, the Globe will have to be manipulated, rotated and moved to get the complete Picture.
And when you zoom down to say City Level, How much of the spherical nature of the Globe are you truly using? At that level, the local terrain is much more important in visualization than the spherical nature of the earth.
Further more, does a spherical model tell the whole story? What about high precision geoids and local datums? How are you going to handle them?
So Globes don't really work when you are interested in details.
We use 2D Maps because they work, if used properly. They have the following advantages over digital Globes:
It is possible to see the entire earth at once. Great Example:
When used with an appropriate projection, you can show and highlight special aspects of Geography.
Attribute based Rendering can be done in a simple way. For example, on a 2D map, you can clearly see that a particular region is colored a particular color. Most digital globes add a virtual atmosphere, often you cannot make out colors near the boundary of the visible earth.
A Digital Globe is perfect when You need to fly and revolve around it. For pretty much any other use, appropriate projections have been developed which are far better for the requirement at hand.