Perhaps a good place to start is using a "western/english" dictionary to define terms that perhaps more properly should be defined by the culture that birthed them.
Why would you be surprised that "eastern/asian" terms might have a bit of ambiguity/less than 100% corespondence with a "western" dictonary meaning?????
"Kata" means something a bit different to Chinese/Japanese/Okinawan applications---its a "form" or "shape" that helps one learn specific skills---everything has a "kata" a "pattern" that helps the student learn---everything from flower arranging to painting to storytelling etc.
So a kata could, from that perspective, have every reason to be a litteral "battlefield" art even if it does not actualy teach you how to cut a man out of the saddle with a glaive...or it could do just that.
My guess is that your mixing terms.
Also not sure that "karate" kata or even many Chinese kata were supposed to be "battlefield" arts...depnding on just how narrowly or broadly one defines "battlefield".....how many people makes a "battlefield?"...3?..5?..10?....1100? Does it have to be on a "field?"...what if its 5 guys in a paved alley fighting with axes and swords? How about fighting on a ship?
NOT trying to be a pain...but maybe your defining "battlefield" a bit loosely?
Japanese koryu "kata" are often litteally "battlefield" arts......not sure that Okinawan or many Chinese arts make that SPECIFIC claim.
So I'm not sure that your base presumption is either accurate or warrented or all that supportable.
My read on your question...essentialy.... are "kata are sutitable for or did they have their origen on the battlefield??
A-Not sure that anybody claims that they are.
B-Not sure that the question---as it mixes terms and outlooks from one culture and then tries to use them to define terms/meanings from another culture in a fashion that might not be all that accurate--is a good way to phase it.
C-Might be a little to narrow in framing.....maybe.
D-Overall--sucess on the "battle field" can mean many things---the army uses a wide range of H+H combat skills--and those folks have GUNS
which are generally superior to even "long bladed weapons" so I'm not sure that empty hand stuff is really uneeded or not worthwhile.
On this point you can argue with the Armed Forces if you like--just not sure that they will care much what you think about how they run their training.
Its probably certain that at least "few" Chinese kata had their origen in "martial" application as YOU use the term.....its certain (with some degree of accuracy) that at least a few of the folks that created/used them were military people so it stands to reason that military experiences were drawn upon to create or train in their kata....hard to imagine a guy/gal saying "sure I spent 20 years fighting in the army but I'm NOT going to use ANY of that experience in working on my kata."
Yes, many Okinawans had offical, semi-offical, and noon-offical contact with various Chinese individuals of various function.
On a strictly personal note...its my belief that "kata" are ONLY ONE section of a training methodology that involves all sorts of training---strength training, heavybag work, resitant drills and partner work, conditioning,sparring/grappling, etc needed for developing fighting/self defense skills.....so in my view Chinese and Okinawan/Japanese kata ALONE are not going to be enough.......the history of the arts rather strongly suggest that back in the day many of the "old masters" did much more than "just" kata to develop skills.
Just an opinion....like always could be wrong