There must have been some car, somewhere, at some point in time that had a fuel pump that was likely to melt down if there weren't 4 or 5 gallons of fuel sloshing around in the tank but I've had a Nissan Pickup, Nissan Sentra, Volkswagen TDI, Saturn Astra, a Chevrolet Malibu and now the diesel Cruze and I routinely drive or drove all of them until fuel was very low and have never had a fuel system issue ) with (or had to push) any of them though in my youth I did literally sputter into a station one time in my old Sentra.
Why run them so low? I can think of a few reasons beyond that stopping to buy fuel is an interruption and in the case of the diesels, messy.... If you use discount points (grocery store, Fuel Rewards etc) you get xx cents off the first 20 gallons or whatever. I often have 40 to 80 cents of discount available. If I use those points to buy 9 gallons of fuel instead of 14, that's a few bucks wasted and those points don't refresh for free. Also, in the case of the Chevrolet's in particular, the fuel light comes on VERY early. In the Malibu I would literally have 5 gallons in the tank if I buy fuel the moment the low fuel alert comes on. That's a big bucket of fuel, way more than I need to feel cautious. I often drive as much as 40 miles after the low fuel light comes on and in 110K miles it has rarely accepted a full 14 gallons which means I STILL have over 2 gallons of fuel plus whatever is in the lines etc. Lastly, I often have Shell gift cards I want to use (another way to earn points at grocery store and some stations give you 5c off and all of them at least give you the cash price instead of credit...) and Shell stations aren't always right next to where I am but are on the way someplace.
I sometimes buy fuel at the edge of PA if it allows me to get where I'm going and back into PA regardless of how much gas I have in the tank. This is about the only time I fuel up with more than 1/8 of tank left unless I'm in Nevada or Alaska where there are some truly remote areas.
I don't expect my eccentric reasoning will appeal to most people. I would say that if you have a 15.6 gallon tank (Cruze Diesel) and you are usually pumping 12 or fewer gallons (assuming you don't overfill which with patience you can easily and safely do with Diesel), that's a lot of useful range you could stretch a tiny bit just to buy at the same station each time or wherever you get a little better deal, etc and still not be running on fumes at all.