Discharge lamps would no doubt be more efficient. But...
not only would you have to correct for color balance, but
the bulb would have to be "mated" to the projector's optical
system.

Large theater projectors are still an arc light?

I'm not sure. I seem to recall that some use some form of tungsten lighting.
Don't hold me to it.


There must be some sort of white/color balancing scheme for
them. Same could be used on other forms of HID illumination.

The "scheme" is simply to have a standardized color temperature. The prints
can then be balanced accordingly.