The economic system that is in place has actually been around for thousands of years. Originally, humankind would trade one item of value for another item. In time, Gold became the currency of choice since it was valuable.
Unfortunately, money will be around so long as people continue to refuse to work simply because a job needed to be, done. The only solution to removing money from the world would be that all people work together for the common good of humankind by doing what needs to be, done versus monetary incentive as envisioned by Gene Roddenberry.
Still, having a better understanding of why money was, first implemented, will also answer the question of why, it will continue to be, used by people. People trade labor in return for money, which actually started several thousand years ago when Egyptian workers were paid with Sala, or Salt. Salt was a valuable commodity back then and today, we use the derivative of the word Sala for Salary.