Uh oh! Both "To WB or not to WB?" AND the "what color temp for lights?" debates all in one thread? LOL
It's an esthetic choice and there's no hard and fast rule, except the physics involved. Depth, w/wo filter, light to subject to lens distance and type of shot (wide, medium, close up etc) and on the camera end, how to set WB are all variables to consider. Plenty of subjects on those issues and it's a matter of combining them for the look the shooter wants.
To keep this short, if one uses a filter on the lens, then using filters on the lights allow the (lit) foreground subject to be balanced to the ambient light WB, since the lens filter is altering the color temp of light hitting the sensor to see less blue/green. The Cyan filter regulates the reds in the lights to attempt to match the ambient light, so the subject doesn't look red.
That works well with fixed distance subjects because your WB is on the lit subject or foreground and the background. Once the distance of the subject changes (say a shark or turtle siwmming towards the camera) then the color shift will be off color to in color as it approaches the light beam, which isn't very useful for a master shot. That's why filters and lights are used mostly on stationary objects like reefs, where the distance can be controlled.
As for color correction and grading, it's definitely an esthetic choice. Océans messed with gammas and different camera profiles for underwater for many of their ocean shoots, because they wanted to keep the blue in. BBC NHU sorta does the same thing for most of their previous series unless there's like shallow reef stuff or macro subjects which can be lit or WB due to distance to lens.
There are films where certain scenes are lit to have skin color and others don't. Into The Blue was a film where the shallow and closeup scenes had skin color and corrected WB, while the wide shots of the wreck etc did not. I mean, all those hot bods would not have looked good all blue, in a blue bikini no less! 
With IMAX films, it's a bit more complicated since IMAX was shot entirely on film and thus there is no easy white balance except in post and lighting. For example, Howard Hall chooses to shoot with the Tungsten (Halogen) lights as an esthetic choice. They could've changed the colors in post easily, so it's obviously an esthetic choice, not a technical limitation. The HMI light banks which have been around for years (at least from the late 80s (remember the Abyss?)) were the choice for pool shots. Halogen was more of a 70-mid 80s thing.
Also remember that using a filter means the filter will be less bright, because the filters are absorbing light. The bigger the shift the more light absorbed (up to 3 stops). Blaise, how much light is loss with a Cyan filter on a 4k LMI LED?
@AY
Hmmm is that the Busch Hippo habitat? I ask because from what I know (which isn't much), every wild fresh water area with hippos wouldn't have such a colorful variety of fish species? 
Anyway, why would you shoot in program and need EC +? is it not easier to just shoot manually and expose using spot metering and histogram, then finishing in post?
And no, RAW does not have WB information set in for still. For video, unless it's RAW codecs like .R3D, ARRIRAW etc, the WB is set off the sensor, even with 3G SDI uncompressed feeds.