Soft magnetic materials are used in core of transformers because the main merits of these materials are relative permeability (how readily it responds to applied magnetic field), intrinsic coercivity, saturation magnetisation and the electrical conductivity. It is used to lower the magnetizing current drawn by the transformer.
Even if both windings are tightly coupled there is approximately no leakage between them, a magnetomotive force is necessary to magnetize the air shared by both windings.
Hence if you compare both inductances (air and soft-iron), the inductance of air is much lower. Therefore, for a given flux linkage the (magnetizing) current will be much higher for an air-core transformer.