The never-ending customer service dilemma: Satisfied client, or satisfied company?

Customer service newbies will reply to the question "What is the most important task of customer care?“ by saying it is customer satisfaction. The more experienced and enlightened people will correctly tell you that customer service means finding a compromise between the requests of the client and the possibilities of the company so that the client leaves satisfied, without the company losing money.

What do top-class professionals in this field think about this never-ending dilemma of customer service?