One small benefit would be that the Amsteel weighs much less than steel. I guess it would save about 200 lbs on some picks where the boom was extended 125'....not much of a benefit really. There are electrical advantages if you were doing work near conductors, but there's a lot of drawbacks to using Amsteel on a crane.
You wouldn't have to lubricate it, but I think it would last for less time than a wire rope that was never lubricated.
I would think that UV rays break it down. There's something else to consider against using it on a crane winch line.
One thing that would be great is to tie all your old worn out climbing lines together with knots and use that as your winch line. Imagine the cost savings from re-using that old worn out rope!
I use 1/2" Amsteel Blue for all of my crane chokers and I don't see any slippage (like Samson says may occur). I think brand new stuff could slip slightly (maybe 1/4"). But, that is not alarming.
But when you start to use it on trees, the bark makes it fuzzy and the slippage stops. I have been monitoring this for about 6 months now.
On the contrary, it can get so fuzzy that saw dust sticks to it like Velcro.
This actually makes it more difficult to untie.
I only use a running bowline with this stuff. And I make sure the knot is dressed nicely. If it isn't, it will be harder to untie after a load is on it.
I have experimented with other knots and they are a pain to untie.
I do feel it slips a bit and you have to anticipate that.
It does get fuzzy and sawdust sticks like crazy.
I am looking for a good cover for it because if a little sharp object touches it, it pulls it apart and it's extremely hard to get it back into the weave.