For professional applications there are sulfur plasma lamps which have a continuous spectrum at high efficiency. Unfortunately they aren't economical below about 1000 watts which is impractical for many applications.

The technology basically works by continuously microwaving (think oven) a small amount of sulfur gas. The development of solid-state microwave emitters — most microwave generation is still done with vacuum tubes — might help miniaturize the devices. However, it's hard to beat the simplicity of an LED.