The biggest disadvantage of using your dive light for lighting your video is that it gets awkward to use it for signaling. That doesn't work very well if the light is set to flood, and lighting a video with a handheld light is a bit awkward.
I'd like to expand a little on this.
Night dives are among my favorite type of dives. I love night diving, and my only problem with night diving is that in my part of the world, night diving means autumn/winter diving, which again means cold conditions and risk of crappy weather.
For night diving, one should - IMO at least, and also according to standards - carry at least one spare (backup) light. "Two is one, and one is none". And since light signaling is THE way to get your buddy's attention (move beam back and forth or up and down in your buddy's field of vision, calmly if it's a non-emergency, quickly if it's urgent) or signal "OK?" "OK" (draw a circle on the bottom with the beam), a narrow beam is really the only good solution. OTOH, as I said, using a narrow beam for lighting video will give you a small hotspot in the center of the frame.
My primary light - a SOLA - has both a spot setting and a flood setting. I've tried using it for night diving videography, but I had to choose: Either use it to light my video, or use it as my diving light. Particularly since I don't like using a handheld light for my video; it usually gets too close to the camera so I get too much backscatter. So I mount it on an arm on my tray, which makes signaling even more awkward. If you dive in great viz, backscatter will of course be less of an issue, but I think it'll be a little tricky to get good, even lighting with a handheld light.
It's of course possible to use your backup light as a primary light/signaling light and the original "primary" on flood as a video light. If any of those lights dies, you still have a backup, and you can abort the dive safely. To me, that was not a good solution. Particularly since my SOLA drowns the beam of my backup, so my buddy will have some issues with seeing my signals. So, I've bit the bullet and bought a second SOLA - which serves as both a video light and as a focusing light for my stills photography.
However, a lot of things are possible, so if you're on a budget, why not try it? Just remember to carry a backup light, make sure your buddy can see your light signals and remember that buddy awareness is important, so don't focus (pun not intended) too much on your videoing
