I'd beware letting a two stroke starve to stop mowing, as the engine is lubricated by the oil in the fuel. No fuel = no oil = no lubrication. I understand residual oil in the crank case will offer some protection but it seems better practice to kill the ignition instead.....
Correct. I've seen rusted bores, on 2-strokes whose owners used the 'run dry to stop' method.
I'd speculate that this practice may have had some point, back in the days before specific 2-stroke oils were marketed. The old Castrol XL used to drop out of the fuel, and settle at the bottom. Now, this can be rectified for the fuel in the tank, by giving the mower a good back-and-forth shake.
But that wouldn't work on the fuel in the carby bowl - if the oil layer there reaches the main jet, it'll extremely hard to start, at the very least.