High permeability core material at high frequency
There's a good reason for the many different materials in transformer cores.  Core loss is one of the many parameters involved in the trade-offs required, and at high frequencies (&gt;500Khz) ferrite would be chosen over the other materials in your chart because core losses would tend to dominate in the other materials you have in your graph.
For a tape-wound material like most of the ones in your graph, the tape is kept as thin as possible to reduce eddy currents in the core.  The construction allows for high flux density, but at high frequencies even 1/2-mil tape would have unacceptably high core losses.  And as @Neil_UK pointed out, there are significant magnetizing losses due to the large hysteresis - remember that this type of loss occurs each time the core magnetization is reversed, so higher frequency means more magnetizing loss.

Source: Magnetics Inc. Tape Wound Core Catalog
Ferrite has acceptable core losses as seen below, but at a price: the flux density at which you can operate will be lower.  Here is a curve of Magnetics &quot;L&quot; Ferrite:

Source: Magnetics Ferrite Cores Catalog
So you will be able to operate at high frequency.  But this is only one of the many considerations you must make when choosing an approach.  It is unusual to choose the frequency first in a power transformer design, but if you have to run at the high end, you are on the right track with ferrite.
Good luck!