A valid point, but not *quite* complete -- eddy current losses are fairly small if you keep delta B small, which is a design parameter. You can choose a large delta B; flybacks run ferrite cores run from ~0T when off, up to 0.3-0.4T to maximize power density. Or you can choose a small delta B, typical of laminated iron audio transformers (which retain permeability up to a few kHz, above which it's mostly the winding structure that determines bandwidth), pulse transformers, CTs, and oversized filter chokes.
Some examples of the latter: many of the machines we use contain iron-cored inductors feeding the inverter ("constant current" supply, not unlike the Baxandall oscillator Slowman has wet dreams about :) ), which have ~500VAC at operating frequency applied directly (>10kHz). Because the inductance is so large (>1mH), the delta B is very small and losses are managable (they rarely have water cooling). Sometimes, these chokes also double as the choke input for an SCR chopper front end, where delta B is large, but the frequency is low.
A more mundane, but less impressive example: powdered iron cores are very common in forward converters (the yellow/white cores). These things just suck. At any usable frequency (i.e., >20kHz), they can't even handle more delta B than a ferrite core of the same size, even though Bsat is at least double -- only saving feature is they are awful cheap. If you wind enough extra that it's biased around maybe 0.7T (lots of energy storage) and runs maybe 0.1T ripple (which will give you low current ripple, despite the drop in permeability at this bias), it'll work just fine. Too bad it's so big and heavy now..
One of these days I'm going to build a water cooled, monolithic, electronically variable ferrite inductor to end all. A few microhenry, couple hundred amps and volts... should be pretty compact, too!
Tim