I have 4gigs of Ram, a triple core 2.8ghz processor and a 460Fermi. The Heightmap tutorial runs at about 15 FPS.

It seems to me that if it takes that much power to edit the Heightmap that it is not practical to use it (as it is used in the tutorial) in a game. Am I doing something wrong, or is the tutorial this slow for everyone?

56 FPS here.

Wouldn't recommend using it for real time editing, only under certain circumstances. and yes it is a very performance consuming process to recreate the mesh each frame.
Pretty obvious this is not how the editor is handling it. ;p

Well, the editor does not need to calculate the physics every frame as well.

It would, however, allow for a cool effect for loading: The world starts flat and morphs into it's shape and texture as you load. Granted, the loading would take longer. Still, it would be a cool effect.