First of all, humanly speaking, aesthetics: your corals will glow different colors under actinic.
Secondly, it is a hunting period for some of your fishes, like mandys, scooters, etc.
Thirdly, you can't keep the mh on too long (I run mine about 7-8 hours) without your tank getting too hot and it sunburning some specimens. Your coral's zooxanthellae appreciate it, but in moderation.
Fourthly, the actinic does have energy to contribute to your corals, and it continues to provide it, in mild degrees, after the mh has gone out. You'll also see your corals begin to fold up or extend tentacles for the night, fish begin to seek their sleeping spots---this provides a quiet-down period for the reef, a changing of the guard for the night.
I don't run moonlights. I have my actinics on 12 hours, with the mh pretty well centered at 7 hours in the middle. Since the reef really doesn't care WHEN it gets this cycle, I arrange it to have the mh off during prime tv hours.