Every fish caught in my boat is gilled and gutted shortly after being caught. This includes stripping the midline kidney from the spine.

That gets rid of all the bloody foul and rapidly decomposing elements of the dead carcass, leaving only the edible meat completely encased in skin and natural membranes. These act as natural barriers to bacterial invasion of the flesh, esp on an extended trip. The fish won't be cut for several days til I get home.

Even with good refrigeration, the single biggest factor in accelerating spoilage is exposure and handling. Once you fillet, the meat immediately becomes exposed.... and it must consequently be handled.... thus inocculating it with all manner of bacteria from your hands and working surfaces. Working on a wet surface facilitates the transfer of that bacterial load by an order of magnitude. The time clock to spoilage is now set to fast forward. Kick it up a notch if you then throw all of the fillets together in a plastic bag to allow exposed flesh to marinate in slime.

If I'm short on space in the ice chest, I'll concede to cutting off the heads and tails, exposing only a limited cross section of meat in the process.

My goal is to delay filleting for as long as possible to maintain shelf life. I cut the fish when I am ready to distribute the bounty to friends/family, or when I am ready to prepare it for my own consumption.

Another reason to gut before filleting is to strip out the kidney tissue in order to reduce bloody contamination of the meat. Even if you bleed the fish very well, there is still a lot of residual blood in the kidney that does NOT run out even with the aid of gravity. That tissue is like a bloody sponge. There are vessels from the kidney emerging at the spine and adjacent to each rib. If you are good about keeping your blade tight against the bones, these vessels will be severed.... and each WILL bleed if the kidney is still intact. There will be negligible to zero bleeding if the kidney is removed first.