So, the question about keeping the sea cocks closed when off the boat, or at other times when not being used, usually has to do with the condition of the attached hoses. Boats have sank, or nearly so, after a hose leaked, broke, or come off a sea cock that had been left open. That could happen if a hose clamp rusted through and sprang off, then some time later the hose worked off, etc. Thus, the insurance requirement for double hose clamps at sea cocks. The doubles might help you get by a lost hose clamp for a while, but one has to notice at some point that a clamp has come off or risk losing the other one as well. So, CHECK your hose clamps and the integrity of the hoses at the barb. The best way to check ‘em is to take ‘em off and closely inspect.
Opening and closing the sea cocks routinely insures that they will operate as required. I normally keep mine closed when away from the boat (out of town) or off the boat for extended period. The ones I rarely need are closed for long periods, etc. The diesel intake is usually open, however, b/c it’s a PIA to close and open as it is a strangely configured needle valve that's hard to reach and operate. (It’s a component of a Yanmar saildrive).
But there’s more. The sea cocks themselves can degrade/deteriorate, leak, break, or become frozen or stuck. So, they should be routinely inspected, and even replaced every couple of decades, etc. If you have a sea cock that does not operate, it should be replaced. I’ve replaced 9 of the 13 (ridiculous number) on my 1999 Bavaria. Three that were swapped out could not be closed b/c the attachment between the handle and the ball had rusted through, or the handle rusted off I could not find a replacement. One down-side of owning a metric boat in the States.