Go to your happy place by picturing yourself in some kind of heavy, sturdy vehicle, like a plump protecting mother of steel.
Given that the military may have to move people even in horrible weather conditions, how would a vehicle crew/platoon go about dealing with this sort of situation?
The safest way to drive through water is to wade the course first to check for depressions and obstacles, but wading has its own risks, so if everyone is to be taught to drive through water, then everyone would first have to be taught white water wreck and rescue, but since those skills require ongoing group practice, everyone would have to devote a significant amount of time, effort and expense to preparing for something that they will not need to use if they are patient rather than bull-headed.
And even if everyone were properly trained to dive through water, most vehicles are not built for crossing water, so everyone would have to learn how to locate differential breathers, air intakes, and electrical contacts on all the makes and models of vehicles that the might drive, despite most people knowing almost nothing of these things in their own daily drivers.
Your proposal is not practicable, whereas teaching “Don’t drive across water” to everyone is. Just turn around and go back, or shut down and wait it out. As you know, patience is a virtue.
I had a dream last night about being driven into deep water. I blame this thread.
… that floats very, very badly. Sleep tight! 
Fear.
the only reason they are out on the road at all is because they are afraid to stay where they are and want to get to someplace else. When they see water/sign, they are afraid to stay where they are, by definition, and so they try. Sometimes it works, sometimes it doesn’t. That it isn’t ever worth trying isn’t something a frightened person can handle.
I was driving in Albuquerque about 30 years ago. When we got a tremendous thunderstorm and the big turn on I 25 north just before the I-25 I-40 interchange was flooded all lanes except for the left most lane. Traffic was backed up as everybody went slowly in the left lane. On guy decided he did not have to wait and drove his pickup into the deep part until the water was about 2 to 3 feet up the truck then he stopped.
By driving large vehicles that were designed for deep water operation (raised intakes & exhausts, high ground clearance, etc.). Some, like the USMC amtracs, are literally amphibious vehicles. They are also trained on how to operate these vehicles in deep water.
I think much of the problem is “familiarity breeds contempt”. We are used to water, we see and use it safely all the time; so we tend to greatly underestimate how dangerous it can be under the wrong circumstances.