The term “combative martial arts” is technically redundant. The word “martial” refers to war, which would seem to be inclusive of combat in some form. Martial arts, however, have come to encompass all manner of styles which no longer emphasize the development of fighting skill. For this reason, I must make a distinction by specifying combative and non-combative martial arts. Opinions expressed for one, are not necessarily valid for the other.
Though this site is primarily focused on the topic of conditioning and breaking, it is important to discuss the basic, effective practice of martial arts. This is not a digression from the topic of tameshiwari. I wish to impress upon you that genuine tameshiwari is indeed a training method for fighting and not a study of parlor tricks. To discuss tameshiwari without considering fighting theory is to entirely miss the point.
You must not forget that breaking is not intended to be a stand alone skill. To practice breaking without relation to combat application is just as faulty as practicing forms without visualizing the applications of the movements. Though one may practice true fighting without breaking, one cannot practice true breaking without keeping fighting in mind.
I will not get into a discussion on particular fighting techniques, as breaking is not limited to any particular style of fighting. Tameshiwari is a tool to be applied in any number of striking styles. It is not a system of fighting, but an approach to fighting. The attributes developed in this form of training should be channeled through your chosen striking art.