There are a number of things that can go wrong in a golf swing. If the clubface is half a degree off, the ball can end up 20 meters off target. If the ball is hit 5 mm off the sweet spot, it will have a detrimental effect on distance and direction. The actions of, and timing of firing, the hundreds of muscles involved must be held in the subconscious memory of the golfer. One may think of this set of finely tuned actions as a software subroutine. Obtaining the required accuracy with one club, and embedding it in the subconscious mind, is an achievement. To create and memorize a different subroutine for each of the thirteen clubs in the bag is next to impossible. The golfer must also be able to differentiate the thirteen routines and call upon any one of them at random. With many years of endless practice, one may get close to mastering this at a subconscious level.
Even professional golfers at the highest level can win a tournament one week, and then miss the cut the following week. It is difficult to maintain the thirteen subroutines. Therefore, throughout the history of the game, people have tried to match golf clubs within a set so that they all will behave as intended, using one swing. One subconscious subroutine could then be utilized for all thirteen clubs. It is much easier to maintain one set of tasks rather than thirteen. Especially when they are so similar that it is difficult to tell them apart.
This discussion does not include the putter, the fourteenth club in the bag, as it uses a fundamentally different set of movement and does therefore not interfere with the subconscious skills of swinging the thirteen clubs.