If a tank is relatively empty, it's possible for air to be sucked into the fuel pump, at which point it could air lock or cause cavitation damage. This is in addition to there being less fuel in the lines which require it to run at a higher rpm to feed the engine. The higher speeds and uneven flow will lead to higher bearing loads on the pump shaft.
Another commenter already pointed out the heat issue since the fluid acts as coolant.
Adding on to eyegor's response, in some instances, a thin layer of sediment can build up in a gas tank as well. This is normally not an immediate concern in and of itself but letting your fuel pump run too close to empty can start drawing in that sediment which can eventually clog the pump. It's worth noting this is more common in vehicles that tend to sit for a longer periods of time, like lawn mowers, motorcycles, and grandma's beige-on-beige 2008 Camry.
So you've knocked a couple operating hours off the life of something that tens of thousands of operating hours? Big deal. It'll be fine unless you run it dry for a long period but you won't be doing that because cars don't run the pump when the engine isn't running.
I have replaced fuel pumps. This involves a lot of work and often a specialty wrench. You will usually need to drop the fuel tank, which requires at a minimum raising the vehicle over 18" into air. The standard 14" jack/stands solution most motorists own is insufficient. They need to be replaced mostly because their integrated fuel filter gets clogged by the sediment accumulated at bottom of the tank, which causes the motor to fail. When the tank has plenty of fuel, the gunk at the bottom of the tank is less likely to be ingested by the system.
For my car, the pump assembly is $900. And then there's the labor charge to put it on a lift, drain out whatever fuel is in there (saving it for later), dropping the tank, and then to remove/replace the bad pump. I would guess an easy 3 hours labor.
With the average used car on US roads now over 12 years old, having the pump go bad could mechanically total some vehicles (the repair cost would exceed the vehicle's worth), so you're going to want to prolong it's life however you can.
This is in the same territory as the advice I see sometimes to make sure you don't turn the steering wheel while the car is stationary ("dry steering") because "it will put stress on steering components and shorten their life, and it will damage the tyres".
These pieces of advice are technically correct but catering for edge cases that won't affect 99% of drivers/vehicle owners. Modern cars are designed for the way people use them; people run their tanks to empty all the time.
I mean, I get your point, but I need to refill my car at some point and there are plenty of gas stations - so why not fill it up early to take care of it?
