As others have stated, the chambering hand is called "hiki-te" and is involved in pulling something back with it into the next technique. Either a limb or a jacket to off balance.
As always there is an apples and oranges comparision being made between karate training methods and sports methods. Boxers have a chamber as well, and there is based on what is best for them in the ring under the rules with big gloves on. Look at how they held their hands in old bareknuckle bouts when they had to worry about low kicks/stomps and hip throws and you will see that it more closely resembles the karate methods. Boxers know they are only dealing with two weapons--right arm and left arm and that it is coming in the form of a punch and those punches are only going to be from the top of their head to just above their naval. Their guard/chamber is based on maximum protection to protect those areas. They also know that they can't grab onto their opponent's limb to pull them. It does not mean that boxing can't be effecive, it's just that it's methods are for a very defined use.
Secondly, karate was based as a civilian self-defense system. It was NOT designed for on the battlefield, it was NOT designed for unarmed peasants to defeat the samauri, and it was NOT designed for two willing contestants who enter into a ring and then square off looking for an opening first. Karate and it's training methods were designed for "normal people" who are attacked by either grab, push, pull, punch (as McCarthy calls it Habitual Acts of Violence) and then you damage your attacker and get away. NOT stand there toe to toe and duke it out. The kata (and other training methods) are ways of dealing with the most common types of attacks that men have used for a VERY long time.
Again, apples to oranges. You are comparing two different goals and training methods to their own unique situations and trying to mix the two.
Here is a VERY good blog on many training methods (basis is Goju-Ryu) and this one is on chambering. Read it and apply WHAT the chamber is really for and it used to achieve.
http://dandjurdjevic.blogspot.com/2008/08/chambering-punches.html