Where you really need white light with a continuous spectrum, there are very few alternatives to arc lamps.
Some time ago there were published some interesting research results, which suggested that it is possible for incandescent lamps to make a comeback, this time at a efficiency comparable with white LEDs. That could be achieved with a carbon filament in a gas mixture that prevents evaporation, where all the inner walls of the lamp are very good mirrors for infrared light, but the front window of the lamp has an optical filter that passes visible light, while reflecting infrared light.
Such an incandescent lamp could have a much better efficiency than an arc lamp, and also a longer life (the very low efficiency of the traditional incandescent lamps is due to most of the energy being lost as infrared light).
It remains to be seen whether that research can lead to commercial products.