#24 or #36 line is not going to stop the boat from pulling/dragging its anchor, its going to snap or drag you with it. It could also do such things as pull the reel from your hand (bad) or snap the line further away from the starting point. So now in addition to having to deal with navigation you are going to have to clean up your line before ascending.
With such devices such as GPS and depth sounders the captain knows where he has anchored, so in the event of the anchor slipping or getting pulled, he will know where to look for your bag.
I suspect you Seattle-its have gotten a bit spoiled on boats. In Monterey, 4 to 6 foot swells is a great day and 7 to 9's are common and boats taking experienced divers out on 12 to 16 foot swells. In such conditions, it can be much harder to see the bag and the Anchor + chain bounce around a lot more.
Speaking for myself, if I am running line I really *really* want to get back to my starting point. If the Anchor is not there anymore then at least the people topside will have a starting point on where to start searching.