Why a transformer can not work with steady current?

Transformers consist of a primary and secondary coil of wire. An emf over the primary wire creates a current through it. A current in the primary wire induces a magnetic field that flows through the nearby area, including through the secondary coil.

Faraday's law says that only a changing magnetic field induces a current. So we need the magnetic field induced by the primary coil to be changing all the time so that we can induce a current in the secondary coil. This requires that the current in the primary coil be changing all the time. And what kind of voltage source changes all the time? Alternating current!

If we tried to use a direct current voltage source like a battery, we would maybe get some current in the secondary coil, but once the current in the primary coil reaches its maximum value, it is no longer changing, and there will be no more induced current in the secondary coil.