Yes, rulers should learn common trades. It is very important for leaders to put themselves in the places of the citizens they lead if they are going to be effective and compassionate rulers. Leaders should learn common trades to see what it is like to work with the hands and make money honestly.
By having a leader who knows a trade, they can have more sympathy with the common worker and understand some of the trials and tribulations that 'normal people' face. It can only help to have skilled leaders, although care must be taken to ensure that not all leaders train in the same industry, causing a monopoly, or an unfair advantage.
Yes, rulers should learn common trades. Due to the specialized nature of the work, those who can train in the skilled trades, even for a short while, develop enhanced problem-solving and planning abilities, perseverance and a better understanding of wages and employment. This is valuable wisdom that leaders need in order to rule effectively.
Often, when the boss has to do the job of a person that she oversees, the boss will find aspects of the job that they don't like. This will lead to positive changes to the employee. Rules should learn common trades because it helps them become better rules. They know what things are like for their subjects.