As you say, if we use the number 1, then we shouldn't wear seatbelts, get fire insurance, or eat healthy to avoid getting cancer, since all of those can be classified as Pascal's Muggings. But if we start going for less than one, then we're just defining away Pascal's Mugging by fiat, saying "this is the level at which I am willing to stop worrying about this".

The point of Pascal's mugging is things that have basically infinitely small probability. Things that will never happen, ever, ever, once in 3^^^3 universes and possibly much more. People do get in car accidents and get cancer all the time. You shouldn't ignore those probabilities.

Having a policy of heeding small risks like those is fine. Over the course of your life, they add up. There will be a large chance that you will be better off than not.

But having a policy of paying the mugger, of following expected utility in extreme cases, will never ever pay off. You will always be worse off than you otherwise would be.

So in that sense it isn't arbitrary. There is an actual number where ignoring risks below that threshold gives you the best median outcome. Following expected utility above that threshold works out for the best. Following EU on risks below the threshold is more likely to make you worse off.

If you knew your full probability distribution of possible outcomes, you could exactly calculate that number.