Hi
I always close my kingston cock when I turn the engine off, straight away. I was advised to do this by an old sailer, his idea was that if you close the inlet, you keep the water in the engine cooling system. If you let it drain out an open seacock, the falling salt water evaporates and leaves a salt rime to build up over time in the cooling chambers bizzos. Mine is raw water cooled, but I assume the same theory applies to heat exchangers.
Also, with the seacock open, if I heel over too much while sailing I can get a gutful of air in the kingston cock, that causes an air lock in the water pump and cooling system, stopping the water pump from pumping water, causing the water lock to burn out, filling the boat with diesel smoke . . . I am lucky with my motor though, if it overheats it seizes up, but after sitting for about 15 minutes it cools and shrinks back to size and away we go again.
I also put a Y-valve to flush with fresh water, but if anyone is thinking of doing the same, don't use a T-valve, there is not enough suction on the water pump, a Yvalve is best. Another good use is if you get an air lock as above, you can prime the other tube on the Y-valve to remove the airlock.