Fuel has weight. If a car is designed so it should always be kept at least 5 gallons full, then you're hauling around an extra 40 lbs of weight at all times. That in turn impacts your MPG.
Driven logically, which is to say, fill tank, drive till you only have a gallon or so left, repeat, you'd spend nearly 1/4th your driving time at less than 1/4th a tank, lowering the average weight of your car, thus raising average gas mileage. Sure, by a tiny fraction... but multiply that by the number of cars on the road, and that fraction would add up to millions of gallons.
Further, it costs fuel to get to a station, and to get back up to speed again after stopping. Fill at half tank means you do this twice as often. Again the gain is miniscule on a per driver basis, but millions of gallons saved if everyone in the country does it.
Wear and tear on the fuel pump is silly, the thing should be designed to run at any level of tank, and probably is, but if it isn't, it's going to be covered by your warranty. If GM has to cover thousands of pump replacements every day because people are driving their cars logically, that will encourage them to design a more robust pump. However, I've driven cars using the "low fuel light" plan for 30 years, and haven't noticed an unusual rate of pump replacement (two pumps in 30 years) so I don't really believe this is a problem, unless it is a new one. In which case, I really want to punish whatever bean counter thought a cheaper less robust pump was a good idea.
When exactly to fill up depends on your situation, it might make sense to fill sooner if you're in some back country area where you might have to drive miles to find a station, and you happen to be passing near one at 1/4th tank. But if you're somewhere where stations are plentiful, there's no real reason not to run down to Low Fuel light every time.