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** For the simple reason that a "transformer" always converts voltages according to the turns ratio on the windings. When you feed an iron cored transformer prmary with a current, the resulting voltage drop is undefined and very non-linear. ** An inductor could be used to measure AC current (at a single frequency) as there is a simple ratio between current and voltage drop ( long as the inductive reactance is much bigger than the resistance). A secondary winding would enlarge the voltage to be measured - but that is no longer a *current transformer* at all and loses most of the advantages.The original idea of a current transformer was to allow safe and simple measurement of high AC supply currents with a standard moving iron ammeter. No rectifiers are needed, no high voltages involved and there is virtually no effect on the circuit being measured.
... Phil