I have a few important reasons outside your vehicle's mechanical behavior to keep your tank half full or better.
Whenever there is a natural disaster, disease outbreak, major holiday, or other reason for a large number of people to leave the cities at once, everyone will want to fill up at the same time in the same place. Keeping your tank on the low side most of the time increases your risk of getting stuck in gas station lines, or running out of fuel when the highways jam up, or other screw-ups that can range in severity from inconvenient to calamitous. Do not be the sucker waiting in a 6 hour gasoline line when an evacuation is ordered. Do not be the poor schmuck who runs out of gas and is stranded when a natural disaster is about to hit. Always, always, always keep enough fuel in your tank to get out of town in a hurry. This is basic emergency-preparedness.
The other reason to keep your tank at least half-full is national energy security. One of the dark secrets of the world's energy infrastructure is that it has very little centralized storage capacity -- creation of government stockpiles like the US Strategic Petroleum Reserve has actually caused the private sector to decrease their storage capacity to just barely cover minor supply shocks and seasonal demand fluctuations. World fuel and oil supply is entirely based on constant pipeline flows and tanker traffic -- if the flow is disrupted by war or disaster for even a few days, localized shortages appear almost immediately. It's actually a very robust system, and the shortfall is always made up via redistribution of existing supply, but there is a considerable delay (1-2 weeks) before supply lines can be rerouted.
So how does this affect you, the individual driver? Gasoline production is very well-balanced with average demand, and enough fuel is always made to supply everyone. The real problem isn't lack of fuel, it's too many people trying to fill up at once. If the media whispers the word "shortage," everyone rushes out to fill their tank at once. You can't top off all the cars in the country in a day. All the gas stations and distribution depots in the country have considerably less total storage volume than everyone's individual vehicle tanks added together. So there doesn't have to be a real supply shortage! Just the threat of a shortage causes people to overwhelm the system, creating an artificial shortage for a week or so until the oil and fuel flows can catch up.
By keeping your tank over half full, you can ride out both real supply shortages (which clear out in a week or two) and panic-induced fake supply shortages (which also clear out in a week or two). Do not be part of the panic. Do not contribute to the world's susceptibility to energy supply disruption. Do your part to improve your country's national energy security by using your vehicle as rolling fuel storage. If everyone always kept their tanks over half full, it would double the world's normal fuel storage levels.