Why dont transformers act as a short when plugged in and not being used?

I think I might know why but Im not sure.Why dont transformers act as a short when plugged in and not being used?The load impedance across the secondary is transformed back to the primary multiplied times the square of the turns ratio.The infinite impedance across the secondary of a transformer that has an open secondary (no load) is transformed back to the primary as an infinite impedance in series with the primary no matter what the turns ratio is. An infinite impedance times the square of any turns ratio is still equal to infinity. An infinite impedance is like an open circuit rather than a short circuit. No current flows through an infinite impedance regardless of the amplitude of the applied Voltage.Why dont transformers act as a short when plugged in and not being used?As I understand, actually it does to START WITH.

But as you know, all physical phenomena requires some time to happen, however small that time may be.

So the story goes on something in this manner.

(1) In the beginning, no current and no flux and so No back emf in the transformer
(2) You switch on, no flux, no back emf (to oppose in-current flow due to the impressed voltage)., So in-Current tend to rush in as if apparently in SHORT CIRCUIT.
(3) As the in-current tends to build up, flux also builds up, and so does the back emf to oppose in-current.
(4) As the flux build-up becomes matured (say in quarter of a cycle), , the in-current tend to die down from its peak value, due to the matured back emf, in say 9/10 cycle, and reaches a steady state value corresponding to the no load current ( under the given voltage condition)
(5) When all matters reaches the steady-state condition, then the transformer start to behave under the explanations given by the two responders ( Mr.Uncouth as well as Adaviel) previous to my response.

The phenomena I described is called the “In rush current of transformer”. If due care is not taken about it, then this phenomena may create some mal operations during switching in , such as blowing of fuses, tripping of breakers etc.Why dont transformers act as a short when plugged in and not being used?the inductance of the windings create a back emf that balances the AC input voltage

But they do use a little bit of power, yes.