So the NDCC's do well in sand and dirt but seem to not be very good for mud or snow.
Not at all true. They do reasonably well in all four of those elements. They require a very low tire pressure for sand and snow.
My comments and statistics show that they are extremely unsafe on wet hard surfaces and hard packed snow and ice. Most often when engaged in hard braking.
Why did/does the military stick with them
They were a compromise when the primary intended use was off roads and on un-improved roads in the late 30's. Bias ply civvy mud/snow tires of the 50's were about the same in that they did well in the areas the NDT/NDCC's did well and poorly on hard wet surfaces or ice.
The introduction of the radial tire here in the USA in the 70's soon caught the military's attention because European military's were already moving towards radials which had been available there for several years already.
Today the radial is the primary military tire.
My personal position is if you want:
1-an accurate resto you need to have NDCC's.
2-If you want an accurate resto and you want to drive it in fair weather you want NDCC's.
3-If you want to drive in all weather conditions on all surfaces and public roads (where other folks can be at the mercy of your control problems) then you should invest in a set of modern tread tires for that driving and keep your NDCC's on the stock wheels for when you wish to show the jeep.