At first sight, the formulas are applicable to the discussed problem. Looking into it more thoroughly, it seems like the author doesn't understand his own formulas and jumps into conclusions.
According to my literature, the exponents in the core loss equation
P = k * f^m * B^n
can be ususally ordered like this 1 < m < n < 2.
This means, that the utilizable power increases with frequency, but possibly not very much. To get full advantage of the high Bmax of silicon iron and iron alloy cores at higher frequency, you need to refer to special low loss alloys.