Low frequency transformer at high frequency
A transformer that's designed for 50/60Hz will not work as a transformer at frequencies much above that.

The core will be designed with laminations 'just thin enough' for reasonable eddy current losses at 60Hz. As the frequency rises, losses in the laminations increase. 400Hz aircraft transformers have much thinner laminations than 60Hz transformers.

Fortunately, as you raise the frequency, the peak flux in the core drops for any given terminal voltage, so the hysteresis losses per cycle in the core drop. However, as there are more cycles per second, the core losses tend to rise anyway as the frequency rises.

By the time you reach kHz, the transformer behaves more as a heater, with the windings coupling the input power into core heating. Pump in enough power and it will get hot, with all the normal bad things that that entails.

If you want to operate a transformer at kHz or 10s of kHz, then you need to switch to a ferrite core material, with higher resistivity (to defeat eddy current losses) and lower hysteresis losses.