This comes up from time to time and I just saw an article on the deficiencies with it. I suppose the first time I heard of this was in the tv show Justified, when an arrogant Crow challenged Raylen to a fight. He would stand 21 feet away with a knife and Raylan would have to draw and shoot him before he reached him with the knife. In the show, he tripped and fell on the knife so I never saw the test in action.
The 21-foot rule was first described by Lt. John Tueller, a firearms instructor with the Salt Lake City Police Department. In 1983, Tueller set up a drill where he placed a "suspect" armed with an edged weapon 20 or so feet away from an officer with a holstered sidearm. Ultimately the theory is that the knife attacker could effectively engage the officer before they could unholster and fore shots to neutralize the threat.
I have seen videos demonstrating this with people who carry with a round in the chamber and those that need to charge their weapon in the event of a threat. A person can easily close the 21 feet prior to charging the weapon. Even with a round in the chamber placing effective shots into the threat would be a difficult task. It's about like a safety blitzing without a strong offensive line. He will sack the quarterback before he can get rid of the ball. If you consider this, an attacker could easily close that distance and take you out of the fight.
The question then becomes, are those attackers at 21 feet a credible threat that warrants the use of deadly force. This is where you may get into league issues of which I am not qualified to answer.
I think this is more important in term of your situational awareness (see the color code article). The point being that even when a threat is 21 feet away you may not be entirely safe with your weapon. You need to consider options such as cover between you and a threat or means or retreat. Is this an absolute rule….of course not. Consider it…think about how long it would take someone at a full run to close the gap between you and them. This also emphasizes the need for regular practice with your carry weapon. Knowing your limitations may make the “21 foot rule” more like “50 foot rule” for you..