Can output transformers be made with ordinary power transformer laminations?

 At your risk. Take all safety precautions. Potentially lethal voltages may be present. 

Surprisingly enough the sound can be very good. See previous post.

Yesterday by the way on the larger transformer the I laminations were separated from the E laminations while music was playing. Bass reproduction decreased as expected. Then E laminations were removed, mid reproduction was decreased as expected by high frequency reproduction was still there. Meaning that the high frequencies can pass through air without needing the metal.

In fact this seems to be more correct. The primary is now a coil without core. Its inductance is low. But since reactance is ohms is proportional to frequency too, impedance is high at high frequencies. So the output impedance of the transistor is not loaded so there is no voltage drop. Therefore high frequencies appear at the primary and since the coils are hugged together energy passes through electromagnetic  induction to the secondary. Or is it electromagnetic radiation?

Mid and high frequencies need the iron so that there would be no voltage drop at the primary of the output transformer. And possibly the circulation of magnetic flux?