Peace of mind also helps alleviate elements out of ones control. Such as idling for an hour or two due to a highway wreck. Often one creeps along thus preventing an opportunity for shutting down the vehicle. Just another reason I see no need to push the limits of frugality.
True, you need to be aware of potential hiccups. I'll admit, I don't have much experience running out of fuel (only once when I was young and mindless and forgot my motorcycle was ALREADY on reserve.) However, as far as I know, running out of fuel is not typically fatal. I've made it 34 years without running out (or getting stressed) so if I do run out once in my remaining 25-35 years, oh well. But I don't plan on it.
With me it's not about saving money (although it does rub me wrong to pay $0.30-$0.40 more per gallon than 30 or 40 miles away, right on my normal route). It's about a number of things; convenience and fuel quality and consistency. You see, if I fill up when I still have almost half a tank, the new gas blends with the old and it's difficult to discern subtle differences in the way my vehicles run on fuel from different stations.