Mike Cartier wrote:
yet if you came to my school and held the pommel while striking, I'd tell you to take your hand off of it unless you want to limit your ability to cut,
Really? hmm interesting.
It has not been my experience that pommeling your grip effects cutting at all
What leads you to this conclusion?
Do you want an academic answer or a practical one? I'll give you both, from my point of view. I do not pretend that these are the only answers, but this is what has worked for me.
Academic: pommels are not made as control surfaces. When both hands are able to guide strike alignment you get a more controlled, more powerful cut. Holding the pommel can also place your hands too far apart on some swords, which affects the ability to extend both arms evenly. When one arm is straight and the other is bent, the bent arm can interfere with control. In my experience, except for the velocity boost you get from the initial launch, cutting with the left hand on the pommel is no better than cutting with one hand, and often worse, since what doesn't help can only interfere.
Practical: I do a lot of cutting and have taught a lot of people to cut. I have seen what changes instantly improve results, and one of the biggest is, "Get your hand off the pommel."
Whether gripping the pommel affects someone's cutting really depends on what their goals are. If your goal is to cut plastic jugs, pumkins, watermellons and pool noodles, then it won't affect your cutting very much, because those targets offer little resistance and few indications of bad technique (but are still a great way to practice when you have no tatami). If you cut tatami and your goal is just to get through the mat then it may not affect it much either. But if you try to get five or six cuts out of a single mat with alternating sides (right, then left, then right, etc.) with precise angles (pick an angle and stick to it consistently, I like 45 degrees) and good spacing, good extension and flat trajectories (something that doesn't matter against mats but would matter greatly against a human torso as failing to do this could result in a stuck sword), then gripping the pommel will, in my experience, definitely affect cutting.
Now this is entirely my opinion, and I am no cutting master (though I've had the priviledge to learn from people who are and most of my opinions come from them). There may very well be someone out there who grips the pommel and cuts better than I do. But if there is such a person, I have no idea how he/she does what they do or how to teach someone to cut gripping the pommel. We can only do what we know how to do. I hold my opinions because adopting them has greatly improved my results, and I share them only to help others do the same. Take what you like, ignore the rest. It's a free country.