Why does an additional primary current exist in a loaded transformer?
If the input voltage is constant amplitude sinusoid, then the core flux is also a constant amplitude cosinusoid, as the input voltage is balanced by the EMF generated by the changing core flux through the primary windings.
This means a secondary voltage is generated. If the secondary is loaded, then a secondary current will flow.
On no load, the core flux is generated by the small primary magnetising current. When loaded, this additional current would cause the core flux to change. However, we know the core flux has to stay constant amplitude to balance the input voltage. Therefore an additional primary current is drawn to cancel the extra secondary current, to bring the total current back to the level of the original magntising current.