The proper role of the CEO is to direct the company so that it makes as much money as ethically possible. A CEO's pay should be in proportion to his ability and success in doing so, better than anyone else can. If his leadership results in a company earning $2 billion a year that nobody else can make earn $1 billion a year, then he deserves a large portion of that second billion. The janitor hasn't done anything special to earn the billion, and doesn't deserve extra because the company is doing well.
In line with the growth of the GDP. His pay should track the rest of the economy when he's spectacularly and uniquely effective? Why?
Angry mobs don't spontaneously generate. There's somebody driving the mob's existence, often planning it well in advance, hoping to gain political power or damage someone or something he hates. Mob members look forward to such opportunities to loot, except for nihilists who look forward to an opportunity to destroy.
Anger or violence as a response to income disparity is irrational, immoral, and self-destructive.
The only "principle" we have is that everyone is entitles to a good life, with food, shelter and health care
At whose cost? Earned by doing what? Your good life, with food, shelter and health care, does not come into existence with each new birth, nor is it pre-existing. It must be made by humans, by their dedicated effort, and it should be retained by the person who makes it or trades their efforts for it. It is not to be taken by you or anyone else with nothing of value to exchange.
All the countries focussed on finding practical routes to achievable goals rather than ideologies are doing rather well.
And the difference between a goal and an ideal is?
Equality of results, and justice, cannot coexist. You can have one, the other, or neither.
A person who does not work, and has never tried to work, deserves nothing. Someone who encourages such behavior, someone who supports such a person (assumed to be an able adult), is destructive of society, and evil.
The direct human action (how curious that you chose the title of the magnum opus of the great free market economist, Ludwig von Mises) that works best is that of the people directly involved, the people who spend their lives working in a particular company, the employer and employees. Anyone in government will know less of any particular company, much less the individuals involved, and so will make much poorer choices (nor does the bureaucrat have any incentive to make the proper choices.) Worse yet, someone in government is likely to be regulating the activities of several companies, perhaps in several industries, and will not only have an even poorer grasp on the situation at each company, but be vulnerable to bribes from companies seeking to get a dishonest advantage over its competitors.
Lack of government planning does not mean lack of planning. It means planning by the ignorant, by those subject to political pressure, by those who enjoy having power over others without responsibility for any damage that may cause, by those with an axe to grind or an enemy to damage, or....
Government enforcing a contract that one party isn't honoring, is restoring the honor of the contract. That a person pays for what he gets and gets what he pays for is the essence of justice. That is moral.
Government forcing a pay ratio is creating an injustice, for either the low paid person will be getting more, through force, than he could honestly earn, or the high paid person is forced to get less than his efforts are worth. That is unjust; that is immoral.
That you do not understand that there is more to a contract than the fallback to government force, is a severe indication of your moral vacuity. A contract helps make an explicit, permanent record of an agreement, that otherwise might be forgotten or more easily misunderstood. Breaching a contract damages a person's reputation; others will be less willing to do business with such a person and his dishonesty will hurt him.
For example, I have several times not bought a product because internet reviews have shown the manufacturer unwilling to honor a guarantee.