When I carry it (not often), I either wrap it around the mast and bungie in place, or tie between the hiking straps. In neither case could I get it loose and throw it in time in the scenario you describe. I could see a slip knot on the tramp arrangement, but that thing is always catching the mainsheet as you go side to side.

Last year I got a ticket from the VA Marine Patrol in our little tin boat for not having a throwable (left it on the dock in a hurry to go fishing) :-(. I was by myself in the boat, and had extra lifejackets which I certainly could have thrown, but he told me the throwable had to have a line already attached. Need to check up on that.

What is a non-attached throwable supposed to do for someone that has a lifejacket on? Gives them a little better visibility, maybe. Moral of the story; forget the throwable, get off the bow (at least when waves come). When I sail with young kids, like to have one older one on the boat; their job is to jump off if a kid falls off, just to keep them company. I guess I don't see floating in warm water on a nice day as a big danger. I'm with you; PFDs all the time every time.