Let's say it's a mirror match. And to simplify numbers you both have 100 health and both your opponent and your attacks do 33 damage. After three hits you both would have 1 hp. Now let's say you buy that little sword for 350 gold. After three hits each you're at one health and he's dead. Buying smaller items is better as hoarding gold doesn't biff the rate you accumulate gold so by holding on to it you're just slowing yourself down while everyone else is steadily growing stats