But these aren't wide band transformers, but supply frequency transformers. There's a lot of interwinding capacitance, which you do have to drive, and that takes more current when you move above supply frequencies.
And the hysteresis losses happen every time the core is driven through it's magnetic field range. Do it more often, and you dump more heat in the core, which you have had to extract from the circuit driving the transformer.
What makes you think that?
You said something like it
"Toroidal types work as well or better than E-cores as wide band audio transformers, without the need for layered windings."