No, they wouldn't. That's why they're not done. If the head were moving at the same speed in each case, then yes, they would. But you are entirely neglecting the difficulty in making the object accelerate. There is a "sweet spot" which varies based on what you're striking, how you swing the object, and how you want the object to strike its target. Yes, as you mentioned, there is also a trade-off for control. But do you honestly think I could hit something harder with a 500-lb hammer with no control than with a 1-lb hammer with control? Not a chance. I couldn't even pick up the 500-lb hammer. So how could I possibly hit something harder with it? Clearly there is a flaw in this line of reasoning. For an easy modern case, why do you make a tennis racket so light to be able to hit the ball harder, even when you could easily control it at several times the weight?
No, not at all. First, I think it's pretty clear I've been talking about rotation. Second, except with modern pistol grips, you generally do not have a straight wrist when striking with a thrusting weapon. For older examples I can only think of the cestus, the katar, and the buckler off-hand. Yes, a thrusting weapon does rely more on the mass attached to it since it has trouble attaining the same speed.
Yes. But as you can see and quoted, I already acknowledged that, and it doesn't change the argument. In fact, if we're just talking about holding on requiring force, it only strengthens the argument from a different standpoint.
Let's look at a specific example. I'll make this relatively similar to a sword. Imagine two metal rods, connected end to end, one being the hilt and the other being the blade. We'll give the hilt one a length of 25 cm and the blade one a length of 65 cm. We'll make the total mass 1 kg (about 2.2 lb of weight). We'll put the center of mass 10 cm up the blade. (I've chosen to use a katana of roughly typical sizes since it doesn't have much extra around the hilt. I've chosen nice numbers at those typical sizes.) That puts the center of the blade and the center of the hilt each 22.5 cm from the center of mass, which is nice to work with. That means both pieces have the same mass. Putting all that together gives us a moment of inertia of 85/1200 kgm^2 around the center of mass and 232/1200 kgm^2 around the base of the base of the hilt (pommel's spot).
Now that we know the specifications of our sword, we need to see how it is swinging. To simplify things let's say it is purely spinning around the base of the hilt, even though it's not quite there. Since you are told to "snap" the blade near the end for a proper strike, this is nearly what happens, so the approximation is pretty good. Even if it's not perfect, the basic behavior we see will be the same. We'll have it swinging at an angular speed wi around this axis of rotation.
Now what happens when this is released just before impact? The center of mass is moving along at vi=rwi=(0.35 m)wi. The rotation rate is wi around the center of mass. (Basically, this is the rolling without slipping situation.) This isn't really different motion at that exact moment, just a different expression of the same motion, for all times afterward it is noticeably different. In the first case we have angular momentum L1=I1wi=(232/1200 kgm^2)wi. In the second case we have linear momentum p=mvi=(0.35 kgm)wi and angular momentum L2=I2wi=(85/1200 kgm^2)*wi.
What is different is the interaction as a target is struck. Now we have to deal with the collision. Let's assume the collision happens over the same amount of time, regardless of the method. How much force is required to stop the motion of the part of the sword that strikes the target? This will allow us to compare the impacts most easily. In the first case, the axis of rotation is maintained by keeping hold of the hilt. In the second situation the axis of rotation passes through the center of mass. With the katana you're supposed to hit about 5 cm from the tip, which is 85 cm from the base of the hilt and 55 cm from the center of mass. (This situation is worse for a cutting sword like the katana than for a chopping sword like a greatsword. But I've been working with the katana and just looked up it's striking point, so I'll keep going. Again, the affect will be the same just smaller.) The first case is relatively straightforward: F1=(232/1200 kgm)wi/(0.85t)=232/1020 kgmwi/t, where t is the impact time. It's not so easy for the second case. You need to make sure the change of linear momentum from the force and the change of angular momentum from the same force stop the motion at that one spot. You end up getting F2=(1kg)(0.35 m+0.55 m)wi/((1+(1 kg)(0.55 m)^2/(85/1200 kgm^2))t)=153/896 kgmwi/t. Let's compare these forces. F2/F1=(1531020)/(896232)=0.75. So 25% of the impact is lost by not holding onto the hilt during the strike, and this has nothing to do with adding extra energy into the swing.
Wow, clearly I knew there would be a loss, but even I wasn't expecting a 25% loss. Many European swords, being designed more for chopping, should fare better. And, as I've said, things like axes will fare much better here. But axes have the directional issue to contend with much more so than do long blades. Anyway, there it is.
Chris
Edit: Out of curiosity, I've started looking into just how small this effect is with an axe. I figured it would be best to attach it here.
I'm starting with a modern felling axe, figuring it's got some reach and might be similar to an axe used in combat. I've decided to push things in favor of the axe since I want to see how little effect there would be. So I'm using the best-case weight distribution on a modern felling axe, for which I can find some decent data. Surprisingly, the center of mass only ends up about 75% of the way up the shaft. (I supposed some using plastics in the handle may be further up, but we want wooden handles.) I had thought it would be a lot closer to the axe head, but apparently not. And that was pushing things in favor of the axe. Comparing this axe to a battle axe, I see battle axes were sometimes longer and sometimes shorter than my 36" sample axe. On the long end it becomes questionable about when it's a battle axe and when it's a pole arm. On the short end it's mostly one-handed versus two-handed. From what I'm reading and from what I'm seeing in photos of real weapons, battle axes were generally lighter than felling axes and the shafts tended to be reinforced more while the heads were lighter. I hadn't expected that. So the battle axe's shaft will be a greater fraction of its weight than the head will be in comparison to the felling axe. So my best-case felling axe is even better compared to the battle axe. Now I need to crunch some numbers as I did above...