When kept, my fish either go from the livewell into the cooler alive or straight from the hook into the cooler of ice. I feel that the fresher a fish is when cleaned, the better it will taste on the table. Yes, 9 out of 10 of my fish are still slightly alive when cleaned and nearly frozen. They all have clear eyes (not cloudy) and red gills. The longer you can keep a fish alive the better, fish can start to decay even before death so ice is mandatory for all of my kept fish.
It is a real peeve of mine to see people keep fish in a bucket with no ice when temps are above freezing. These fish are rotting and unfit to eat in my opinion.
I personally would rather die of hypothermia than blunt trauma, and that's the way my fish are treated as well.