We often reach before we think about it; we reach spontaneously. If reaching (and consequently loading the sensitive nerve) aggravates the pain then repeated inadvertent reaching continually aggravates and kindles the underlying pathophysiology. Once the reaching has taken place it is too late to stop it. It may then take hours or days for the resultant pain to settle down again.

The brace limits how far we can reach and so it prevents the inadvertent reaching; we have to move closer to the object that we want to pick up.

If one uses the analogy of a camp fire; the pain is the flame of the fire and the coals of the fire are the ongoing pathophysiology that leads to the sensitisation of the nerves and hence the pain. If fuel is repeatedly thrown onto the  fire;  the fire will continue to burn and the flames will persist. The coals will remain red hot until no fuel is being thrown onto the fire. Reaching is the 'fuel' that keeps the 'fire' burning in the radial or median nerves. 
The brace limits reaching; stops the fuel being thrown onto the fire and allows the coals to gradually cool down; no more flames. When the coals are cool then fuel can be thrown on the fire without it flaring up. So once the fire is 'cool' people can resume reaching again without producing the painful reaction.