I've done it.
Would only recommend this in SALTWATER.
Not sure why they do the initial pressure bleeding with the kidney still in place. The kidney holds a LOT of blood (even after pressure bleeding) so why not take it out from the get go.
Most folks will insist on bleeding their fish immediately after being caught, but some prefer to fillet them later without gutting them out ( they like the extra support of the guts when filleting the belly section). Whenever I have done this, the residual blood in the kidney virtually always oozes onto the flesh. This is why I prefer to gut/gill and remove the kidney prior to filleting.

One guy said leave guts in for back-pressure. Really no need for this as the entire venous tree will be freer-flowing if guts are out. I've gutted and removed the kidney, applied the flush, and have all the cut vessels spewing flush water along the entire length of the abdominal cavity like a garden sprinkler.
Leaving guts in creates enough back-pressure that your flush fluid starts to backfill into the meat. I do not believe water logging the flesh in this manner is good for the meat on your table.
This is the main reason to NEVER do this with river water. You'll be infusing the meat with whatever sediment/contaminants are in the river
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