Learned this when I commercial fished for Speckled truly and Red fish on the gulf coast of south Texas back late 60's early 70's. Putting those fish on ice while they are alive causes all the blood to be drawn into their vital organs thus most of the flesh will be blood free and meat staf fresh longer. In those days we cut out the gills, cut a slit down the side of belly and removed guts. The heads were left on for two reasons, main reason they were displayed on a bed of ice in the market and if you left the spinal column intact you didn't have the moisture loss from the flesh. No reason to not put them on ice for a day or so before cleaning. I always do as others, fillet, put in bowl of water to fridge a day or so then cook or freeze.