I guess my perspective on this is totally different. I do completely the opposite of the general consensus on this thread.
I never turn off the fuel shut off, I never run my carburetor dry on any of my equipment--1948 Cub, mowers, leaf blower, weed eater, chain saw, standby generator, snow blower, etc. I have done this for 40 years and never had a problem ever starting any equipment due to a fuel problem. My idea is this--When the you run an engine until the fuel is gone, the carburetor is dry--if there is a little gas in the bottom of the bowl, it will get stale quickly. Also, I noticed on my gas can, where the gas evaporates on the side, there is a film that builds up, over time, due to the volatiles from the gas evaporating. My solution is to always keep fresh gas in the equipment. On any equipment, that I have not used, every two months (or at the most 3 months) I dump the gas (or siphon it out) and add fresh gas and fill the tank full. I then always start the engine to draw fresh gas into the carburetor. Keeping the carburetors full of fuel also keeps any gaskets/seals “wet” so they do not dry out and leak.
John M.
P.S. I understand if your carb on the Cub is dripping fuel, you need to shut of the fuel. I had that problem and fixed the float so I can always keep the shut off open.
P.P.S. I also filter all my gas with a funnel that has a fine mesh screen--so fine that water will not go through, but gas will.