Although I use amsteel on my little slow 12k winch, it never sees the same kind of usage that the loggers put on. I agree, it melts under shock loading, and it shears much easier than wire rope of the same size. I get it. And DAMN! It is entirely too expensive if it doesn't last on the job.
I should have been more specific with my question. Amsteel (of the same diameter) is a whole lot tougher and stronger than the 9/16 stable braid rope.
Myself, I figure that it's fragile nature compared to a real wire rope is more than compensated by it's ease of use. I can coil my little 3/8ths rope up and toss it 50 feet down a hill with just the weight of the hook. When I break it, I can fix it on the job in just a few minutes, and I don't waste the whole length. I'll get 2-4 years out of one little 100' length, and it never rusts nor kinks. It really sucks to get off the winch drum when you break it, however.