Conditioning is a process through which you strengthen a part of your body. This does include the desensitizing of the nerves to dampen the pain response, but the most important result is in the actual reinforcing of the physical structure.
I do not consider the desensitizing aspect to be a priority because pain, alone, can be mentally blocked. Really, with the rush of physical exertion, pain is not a concern.
Pain is a concern in that it is an indication of injury. Injury is something to be avoided. If you are performing breaks, but breaking yourself in the process, you are not keeping in line with the purpose of tameshiwari. Breaking is a method of increasing power and strengthening the body, not weakening it. It should not be a demonstration of masochism. The proper reason for not experiencing pain while conditioning and breaking is not in mentally blocking it out, but in increasing the durability of the body so as to avoid sustaining injury. There is no pain because there is no injury. This is accomplished through a consistent and progressive training process.
The body naturally responds to stress by reinforcing itself. We know that weightlifting results in increased muscle mass and bone density. Conditioning takes advantage of the same mechanism by applying gradual impact stress to an area of the body. This causes the body to respond by increasing the soft tissue strength and bone density.
As with weightlifting, this stress must be applied gradually and consistently. This way, the body has ample opportunity to respond so it will continue to strengthen over an extended period of time. Training all at once, but only once in a while, will result in stressing the body to the point of injury and does not encourage it to build properly.