Carl - with respect to your training - I strongly disagree. Evaluating the two risks: the risk of a valve becoming frozen in an open position versus the risk of becoming confused and diving a partially or mostly closed valve.
Weighing the likelihood and importantly the consequences of each event:
Stuck Valve Risk: with modern K-valves that have not been abused - the likelihood of a frozen open valve is pretty remote. In the event that it did freeze open - the consequence for a recreational diver is a minor inconvenience. They will have to drain the cylinder before they can remove their reg - but then the cylinder is off for repair - and the diver can proceed with their next dive. A tech diver may have a more serious issue - but will hopefully be self reliant - or have a team member capable of assisting them if they are having a catastrophic failure requiring valve shutdown underwater.
Partially Closed: The path to failure here is to become confused about either how much one should open the valve - or worse yet getting turned around and making the mistake of FULLY CLOSING THE VALVE and then opening it back up a quarter turn! The consequence of this is a valve that may breath at the surface - but at depth could become increasingly difficult to breath - leading to panic. In my experience, the likelihood of this failure is substantially higher than a stuck open valve. I recall a tech instructor teaching a solo class who became confused when manipulating my manifold and turned off all of my valves (including the isolator) by mistake while I was doing a mask off drill.

It was annoying - but not catastrophic. I'd assert that Recreational divers are even more inclined to get turned around and crank the valve the wrong way. If they fully shut it off - its pretty obvious. But if they turn it off and then crack it open - it sets up a diver for a nasty surprise. I would argue this is a lot more common than the freezing of a valve. The consequences are also much more severe. Hence - this is a scenario - I would argue - it would be preferable to avoid.
I'm not a Navy trained engineer, nor do I have specific experience with the valves you may manipulate in the course of your work. However, in this case - the practice of leaving a K valve partially open to protect against freezing the valve - is not sound. In my training and experience as an engineer - it's important to realize when to use a pattern - and when it no longer applies.
Bjorn