The far field is a traveling wave, once generated it radiates away from the source off into free space. The near field is a standing wave, which stores reactive energy. Your question as to why coupled near fields load each other and coupled far fields do not is not exactly correct; they both load each other in different ways.
For example, the transformer you described is coupled by a mutual inductance, a reactive coupling. An antenna has a radiation resistance, typically describing its ability to radiate into free space. This is a resistance and not a reactance because the power is lost. It radiates into space unlike the near field, which is stored. If radiating antennas are very close, they will load each other both reactively and resistively since they will be in each other's near and far field. The Yagi-Uda antenna is an example of such a case where mutual impedance must be taken into account for proper antenna design.
For practical communication purposes, however, antennas are usually too far to load each other. Which makes sense, because the power received is many orders of magnitude below the power transmitted.