Another reason sometimes used to justify holding the non-shooting hand close into the chest is to reduce the potential for having the non-shooting hand & arm move or swing in such a manner that it might cause a corresponding swing, tremor or counter movement in the shooting arm. A balance/counter balance condition.
While being tightly pulled into the body might lend some stability to the extended shooting hand/arm, sometimes the circumstances and conditions might require the use of the non-shooting hand to perform some other role, too. Keeping it out of the way of rounds fired by the other hand is certainly a primary consideration, too.
Some of the older methods may not be as obsolete as some folks might think.
The use of sights is still a good thing, too.
I recently had the chance to attend the CNOA's 2009 training seminar in SF. During the "I'm Shot" 1-day lecture 3 cops were guest speakers. All of them had survived shooting incidents in which they had been seriously wounded, but had been able to continue fighting. (One was the female LAPD officer who suffered a .357 Magnum wound to her chest and returned fire on her attacker, hitting him 4 out of 4 times and ending the incident.)
While the situations and conditions of the shootings were different, the one thing that each of them had in common was that when they used their sights they made hits. Two of the cops said that they had to settle down and remember to aim before they made their hits. One gent said he burned through a couple of mags in his issued .40 pistol, missing when hurriedly shooting at his attacker 'instinctively', before he 'settled down' and aimed, at which time he hit his attacker.
Some of the older methods might still have some relevance. The wisdom is recognizing which are useful, which can be improved upon and which might be replaced with better alternatives.
We're still just shooting a handgun, you know.