Let's see:
Imagine you have a transformer with nothing connected do the secondary winding. If there is no current flowing in that winding, you could just remove it and it would work the same. Now, what is the difference between a transformer without the secondary winding and a simple coil? Answer is: none. What limits the current in a coil? The resistance and, with AC current, the inductive reactance. That reactance is due to the electromagnetic phenomena you describe.