A soldier must have a skill in striking but most importantly have to be a good wrestler/grappler. Wrestling have been an important part of every warrior from ancient times and the reason is that against a decently trained soldier with an armor the striker will have problems. The Japanese warriors found a good solution in training Ju-Jutsu together with their training for their Katana and short sword. Romans, Spartans, Mongolians, Turks were all good wrestlers.
Without separating from the tradition I think the best solution for a soldier is a combination of Anatomy/Vital points knowledge, Biomechanics knowledge, Muay Thai striking techniques combined with a technical training on Japanese Ju-Jutsu locks, throws and good knowledge on a Brazilian Jiu-Jitsu ground work. Instructors should explain that all the principles learned in the unarmed combat are also valid for armed combat. Soldiers must learn that the principles of movement are all the same while both unarmed and also armed with a knife, baton or other means of support. A soldier must know how to fall safely also and minimize the taken damage. It sounds complicated but for the ordinary soldier an arsenal of a couple of basic techniques in these aspects but worked to proficiency can achieve miracles and teaching these basics will not take a lot either.
At the moment the system in which our soldiers train is not bad but I can't say a lot of good things about the instructors. The poor work of the instructors is visible when you watch the soldiers demonstrations. For the untrained person it looks cool but for one that have experience in martial arts the amateur level is clearly visible. Soldiers are made to do techniques that require a careful work of the instructor to early and the result is half learned technique and amateurish application. This is not only a problem in the TSK but all over the world. People are neglecting close combat training because modern armies rely on their weapons and the chance of hand to hand combat situation is not high. The true way is to teach basic techniques to the soldiers, make them practice and do light sparrings at least once a week. They will both learn to fight with time but also the combat spirit and self-confidence will increase. That type of training can be of crucial importance in situation of civil disturbances, arrests in the course of their work, controlling aggressive unarmed civilians and for conscripts the skill learned can prove useful in their everyday lives in situation of self defence or prevention of light crimes.
