One of the first swords I ever made was of A2, and it passed every test a highly qualified martial artist could put it through, including cuting through some serious amount of bone. It was too heavy, and lacked the speed of my later swords, but the steel held up in tests that are normallly applied to swords. I think the rub is in those "traditional geometries". Flat ground blades require a distal taper to get them to balance; hollow ground blades can maintain a heavy spine throughout their entire length. The same guy who tests my blades has tested blades (fighting bowies) from other makers and has broken some flat ground blades made with A2, 5160, and 1084/10N15 damascus. In all cases the blades failed at the point, where they were just too thin to support heavy impacts. In all those cases, the makers were able to reprofile or make a new blade to handle the stresses, but the cost was length and/or balance.
Here's a pic of an 20-1/4" A2 Espada that weighs 18 oz. total. It's made with 3/16" steel and because of the deep hollow grinds maintains that full width to about 3-4" from the point, and only narrows significantly in the last inch or so. The balance point is about 4" in front of the guard, but because the whole thing is so light it feels like an average size bowie knife. For the Filipino style of fighting, speed is life.
The thickness of the blade at the edge is about 0.080", because the apex of the hollow grind is well above there, allowing the grind to flair at it approaches the edge. This provides a heavy convex edge that tolerates impacts while cutting well. The blade is slightly thinner about 1/2" above the edge than at the edge.
If you look at the composition of CPM-3V it is an unusual high alloy steel. It is 0.8% Carbon, 7.5% Chromium, 2.75% Vanadium, and 1.75% Molybdenum. With the Vanadium occupying a good portion of the Carbon, most of the Chromium is free. This is an extremely fine grained steel. In fact the grain structure is so fine, it won't take a polish because the grains scatter white light. CPM-1V is even better, but you can't get it in anything besides blocks. It's impact toughness is about twice that of S7. I have a 1/4" slab of 1V, which I saw on for a few minutes each week. One day it might make a blade.
You probably won't like grinding 3V. When I make a sword from it, it is a very full day at the grinder and about 3 days of aching muscles after that.