AFAIK, their main purpose is to add some blue light (which you can do just as well by selecting 14k/20k MH bulbs) and to show up your corals' fluorescence (particularly noticeable when you only have the actinics on). Your corals will do fine without actinics if you can live without the fluoresence light show.
A 6500K bulb contains enough of the blue wavelength to support corals. However, I cannot stand to look at a tank solely lit by 6500K bulbs. Way to yellow IMO. I use Iwasaki 15K bulbs and they too need actinic supplementation for my viewing eye. I also love the look of the phoenix 14K's but they look even better with actinics, but I could live without the supplementation.
As others have stated, actinic lights, which really are just specialty lights to provide additional blue spectrum light, are not a must have.
That stated the best tanks i have seen always have supplemented with actinic and used actinic for dusk, dawn, and they also assist with the reef keepers light law: You can never have too much light on your corals....
