I'll take a stab at it. (im a wire user). (though will go synth soon just for the weight and safety factor)
Synthetic rope can collapse and deform in a rolled position more than steel. It has the ability to hold onto moisture a little bit more. The weaving is tighter, and thereby can hold more moisture than wire strand.
Steel also dries quicker around enviromental factors- it has more air pockets for air to circulate- the steel readily heats up in the sun, and conducts the heat all the way in, and dries itself out. Synth heats up, but it doesn't conduct heat very well. You theoretically can provide some limited internal drum brake cooling with wire rope, where as Synth would be more of an insulator.
The drum can and will rust. I don't think a little bit of rust will hurt anything, but it will abrade the line, somewhat. How much, Depends on the pitting and rusting level.
I'd take the line off, mask off the area, and wire brush/sand the surface. Get some zinc chromate, and spray on a few coats. Top it off with whatever epoxy based or enamel based top coat you like. You can use etching Zinc primer (some call it cold galvanizing) in a pinch, but a guy who does boats for a living sold me on zinc chromate.
let it dry fully (a few days preferably to harden up). Then respool. Only when the line touches or abraids the drum (or drum sides) should the paint come off. In which case, you'll have to do this process again at a later date.
BTW, there used to be some cause to believe something about the electrical system causing vehicles to rust. Not sure.