I can't comment on filter use below the water line. However, with drop in filters where the filter is behind the lens, I'm seeing a lot less ghosting, flare and refelcted artifacts in my images. Particularly in direct sunlight or harsh lighting.
No use of filters below the water except when shooting fluoresence when a yellow barrier filter is required. All about getting light in and (generally) freezing the action. For "long exposures", you use rear curtain sync and 1/20s-1/50s to blur the background. No reflection reduction needed so no CPL.
EDIT: the above is correct for stills underwater shooting raw and changing white balance in post to taste. eg I don't try to change white balance for deep/shipwrecks as the blue seems to be more natural.
For video, then manual white balance is needed at each depth/distance to subject. For gopro etc, pink/red filters are used to approximate the change in available colours at the detriment of available light. Gopro doesn't recommend using filters at 30m for instance.
Adding strobes/video lights also means that no filters are needed. The difficulty with artificial lights are that there ends up being 2 different temperatures ie daylight for the foreground but ambient in the background. It is generally okay if the ambient colour and shadows are blue but I don't like it when green so I will desaturate the background in post in those situations.