I am not sure that the flushing removes carbon. It stands however to reason that the flushing at the end of the hard work prevents carbon building.
Let's look at it a bit closer.
A while ago I did a heat evaporation test of all oils I had accumulated over the years. I used an electric iron for that. First I coated the iron with black ink, and turned the heat on max. With an IR gun I traced the hottest part at 220°C. +- 2° over 15 minutes. In the hot spot I Dremeled a shallow cup that could hold about two drops of oil. Diameter was about 8mm. (I must have pictures somewhere)
With iron cold and level I applied one drop of the oil in the cup, and then turn on the heat. At about 80°C many general use 20-weight two stroke oil flash off, visible by a smoke plume. These are the hydrocarbons mixed in the oil to make it thin, and improve the oil/gas mixing. 30-weight two stroke oils also flashed, but at slightly higher temperatures. The thicker 50 weightall out racing oils did not flash off until well over 140°!
During the heating up, one could observe how the oil crept over the edge of the cup. The amount of creep is a measure of the surface tension, and the ability of the oil to wet a surface.
Now to the interesting part.
Some oils flashed off completely before reaching 200°c!! Gone! Nice and clean with hardly a trace but some ash. (metal salts)
The other oils thickened slowly, until completely reduced to a film of varnish (brown or black). The rate of evaporation and thickening again depending on oil quality. Castor and Elf racing showed the longest retention of tackiness, while Castor needed longest to turn all black.
When tacky at 220°, and allowed to cool down,the oil was quite firm at low temperatures. Firm enough to hold a ring in place (ring sticking) in a cold engine. This could cause blowby, until the engine warms up. Blowby is detrimalto any engine. It scours the surface clean of oil.

Now imagine the choke stop method. Some care has to be taken on reed engines, not to do it from high rpm.
The still running and warm engine is flushed with a lot of fuel, containing some fresh oil. (some, not much). This thinned fresh oil is carried between all sliding surfaces by capillary action, and mixes with, or coatsthe thick goo that was formed in the hot engine, effectively preventing the rings to stick.
In the next cold start there is no thick goo between parts that prevents the flushing by the fresh engine choke, and the rings are free to move. The fuel/oil mix is free to enter all crevices and do it's job from the first engine revolution onward.
The same is more or less accomplished by the full choke start method. Choke on, ignition on, flip until burp. Choke off, and start.
The only drawback here is that the engine now is cold, and the old oil goo is much harder, so it will not as easily mix with the new charges. So the thickening process goes on, until carbon is formed.

This is my opinion and reasoning behind it.