Because the idle setting with the mixture at full rich is richer than when you lean. Pull it all the way and fuel flow stops. You can see, feel and hear the difference when you lean on the ground. It's absolutely leaner than with the red knob all the way in.
Sure, but when does that happen? As soon as you start pulling the mixture knob ... or the very last fraction of travel before it stumbles?
The correct answer is the latter. If it happens as soon as you start pulling the knob, your engine is not properly set up.
If your engine is correctly set up according to Lycoming, pulling the cockpit mixture control has no effect at all for the first inch or so. There should be no change in power, sound, or temperature. That is because the mixture set by the idle adjustment is already leaner than your manual setting. Turning the mixture control does not make the mixture any leaner.
If you do it according to the engine operating manual, the idle mixture is already close to peak, within 20-50 RPM. If you turn the mixture control Vernier very slowly, you will see zero change in performance until you get very close to the end. Then you will see a very short rise in RPM over maybe 1/4 turn on the mixture knob, followed by a sudden drop off to rough running.
If you do not see this behavior, then Lycoming says to adjust your idle speed and mixture until you do.
Once set up that way, you are already running lean enough in idle to prevent fouling, according to Lycoming.
Per my comment to Half Fast above, I'm not familiar with how much the idle mixture enriches when the throttle is advanced to 1000-1200 RPM. I concede that may be an area where some adjustment may be prudent. But IMO, the majority of ground fouling issues are due to the idle mixture adjustment being improperly set. Rather than compensate for this with manual adjustment, Pilots should be taught to check the idle mixture adjustment and correct (or have it corrected) if necessary.