Thinking about shooting underwater, I feel I should have a larger sensor to capture as much light as possible, whether using a strobe or natural light.
While this is the conventional wisdom in land shooting, underwater we have a number of additional factors that invalidate it. Most of the shooting is either ultrawide/fisheye or macro, and in both cases, large sensor cameras have drawbacks that go a long way towards offsetting their advantages. In ultrawide, shooting through a dome, you are capturing a curved virtual image created by the interface of water, dome glass and air, and the curvature of this image tends to fall out of the large-sensor cameras' limited depth of field, producing soft corners. The domes are also large, heavy, expensive, difficult to travel with and maneuver underwater. In case of macro, when you have a subject that is significantly smaller than your sensor, you have to magnify it by a lot with close-up lenses, and this limits your depth of field. You may get great detail on the small part of the subject that is in focus, but the rest of it will be lost in the blur, while a TG-6 will capture the entire thing.
You also don't need to capture
all the light - you need just enough to properly expose the background (which may be nothing at all, if you want to keep the background black) then add enough strobe light to properly expose the foreground. I was at Richelieu Rock in Thailand just yesterday, shooting my Sony A6300 with 16-50mm lens and Retra Pro strobes, and I was cycling between 6% and full power on the strobes and f/8 to f/36 on the lens, with shutter speeds between 1/50 and 1/160, all depending on the shot I wanted to take.