I always roll up straps and stow them, I also don't leave chains on the bed, sometimes I have strapped a tarp or two down to the front of the bed, but even they need to be put away, just depends on how far your going.
I remove them and roll up then rubber band em. Theyre much easier to throw accurately when you hook first then throw a roll, especially in very high wind. And when you run them through the winch with only one wrap of diameter theyll get way way tighter vs whole strap on winch. I tuck the tail slack under the work end to pad the trailer edge.
Leaving all 40' on the winches means youve got to tighten all the slack before they snug up, and youll notice the straps get a goofy cupping sorta wavy stretch pattern over time.