[magicalhippo]

We say a changing current in one coil of a transformer induces a current in the other coil. It does not control the current of the other coil.

Any induced current is superimposed on top of whatever is already there on the other side. This is different from controlling the current.

For example, you couldn't block DC current passing through the secondary side regardless what you did on the primary side.

[amelius]

Imagine i have a pencil which I'm holding in my hand. With my hand, I can control the position of the tip of the pencil. Now imagine the pencil is made of rubber. I can still control the position of the tip, but e.g. a strong wind can cause the pencil to flex and so the control is not perfect. But it is still control.

I don't see how this is fundamentally different from controlling the current through a transformer.