Like I have said many times before, your fuel pickup is at the bottom of the tank regardless of how much fuel is in your tank. If you have any debris in the tank that will cause a problem when on fumes, you will have that same problem when you have a full tank.

The real reason to not run less than a 1/4 tank is the fuel pump uses the fuel to cool itself. If you run low a lot, you run the risk of burning up the fuel pump.

I run mine 100 - 120 miles past DTE on every tank.

I've heard that even though the gas comes in from the bottom of the tank, the junk floats at the top. When you are running low on fuel, the top of the tank and the bottom of the tank get really close together, thus you are more likely to get a clog. In addition (I'm not a mechanic) I've heard that the fuel pump has to work harder (less pressure) when there is less fuel in the tank and (a traditional gasoline engine) can hesitate when accelerating. I notice that my car does this a lot when I am running low.
Short of trying to get into the 700 mile club (the mile high club is a better accomplishment) I'd advise against running the car with an empty tank. Remember, I am not a mechanic.

What do you think floats on the top?

Dirt? Heavier than gas.

Water? Heavier than gas.

Oil? Heavier than gas, and would actually mix with the gas.

I have never seen any "junk" floating on gas. All the junk I have ever seen was a layer at the bottom of gas cans.

The hesitation is probably some air being introduced into the fuel supply from running very low and the fuel moving to the back of the tank and uncovering the fuel pickup.